50+ Math worksheets for 10th Grade on Quizizz | Free & Printable - Free Printable

Let’s solve each problem step by step.

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Problem 1:
If \( f(x) = 2x \) and \( g(x) = 2x^2 - 1 \), find \( f(g(3)) \)

Step 1: Find \( g(3) \)
\( g(3) = 2*(3)^2 - 1 = 2*9 - 1 = 18 - 1 = 17 \)

Step 2: Plug that into \( f \):
\( f(g(3)) = f(17) = 2*17 = 34 \)

✔ Answer: A. 34

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Problem 2:
If \( f(x) = 2x \) and \( g(x) = 2x^2 - 1 \), find \( g(f(-1)) \)

Step 1: Find \( f(-1) \)
\( f(-1) = 2*(-1) = -2 \)

Step 2: Plug into \( g \):
\( g(f(-1)) = g(-2) = 2*(-2)^2 - 1 = 2*4 - 1 = 8 - 1 = 7 \)

✔ Answer: A. 7

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Problem 3:
If \( f(x) = 2x \) and \( g(x) = 2x^2 - 1 \), find \( f(g(x)) \)

This means: plug \( g(x) \) into \( f \)

So, \( f(g(x)) = f(2x^2 - 1) = 2*(2x^2 - 1) = 4x^2 - 2 \)

✔ Answer: C. \( 4x^2 - 2 \)

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Problem 4:
If \( f(x) = 2x \) and \( g(x) = 2x^2 - 1 \), find \( g(f(x)) \)

Plug \( f(x) \) into \( g \):

\( g(f(x)) = g(2x) = 2*(2x)^2 - 1 = 2*(4x^2) - 1 = 8x^2 - 1 \)

✔ Answer: D. \( 8x^2 - 1 \)

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Problem 5:
If \( f(x) = \frac{1}{x} \) and \( g(x) = 3x + 2 \), find \( (f \circ g)(2) \)

That means: \( f(g(2)) \)

Step 1: \( g(2) = 3*2 + 2 = 6 + 2 = 8 \)

Step 2: \( f(8) = \frac{1}{8} \)

✔ Answer: A. \( \frac{1}{8} \)

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Problem 6:
If \( f(x) = \frac{1}{x} \) and \( g(x) = 3x + 2 \), find \( (g \circ g)(-4) \)

That means: \( g(g(-4)) \)

Step 1: \( g(-4) = 3*(-4) + 2 = -12 + 2 = -10 \)

Step 2: \( g(-10) = 3*(-10) + 2 = -30 + 2 = -28 \)

Wait — but looking at the options in the image? Actually, the user didn’t show options for #6, but since we’re solving it, let’s just compute correctly.

But hold on — the original image cuts off after question 6, and no multiple choice is shown for #6. However, based on standard Quizizz format, perhaps the student only needs answers for 1–5? But the instruction says “solve the problem accurately” — so I’ll assume all 6 are to be solved.

Actually, rechecking: The user uploaded an image with 6 questions visible, but only 1–5 have full multiple choices shown. Question 6 is cut off — no options visible. But since the task is to solve the problems, I will solve #6 as well.

So:

\( g(g(-4)) = g(-10) = 3*(-10) + 2 = -30 + 2 = -28 \)

But since no options are given for #6 in the image, and the user may not need it, but per instructions, I must solve what’s there.

However, looking back — the user said “Solve the problem accurately.” and the image shows 6 problems. So I will provide answers for all 6.

But wait — in the initial request, the user included the image which has 6 questions, but only 1–5 have answer choices fully visible. For #6, since no choices are shown, maybe it’s incomplete? But I should still compute it.

Alternatively, perhaps the user expects only 1–5? Let me check the original prompt again.

The user says: “You uploaded an image containing a task. Solve the problem accurately.”

And the image clearly labels 6 questions. So I will solve all 6.

But for #6, since no multiple choice is provided in the image, I’ll just give the numerical answer.

Actually — wait! Looking again at the image description: In the text you pasted, question 6 is written as:

> 6. If \( f(x) = \frac{1}{x} \) and \( g(x) = 3x + 2 \) find \( (g \circ g)(-4) \)

No options listed. So perhaps in the actual quiz, options exist, but they’re cut off. Since I can’t see them, I’ll just compute the correct value.

But to follow the format, I need to pick from A/B/C/D if available. Since none are shown for #6, maybe the user only wants 1–5? Or perhaps I missed something.

Wait — in your message, you wrote:

“User options:
- ExplainAnswer: false
- TeachTopic: false
- GeneratePractice: false”

And then “Response format rules” say to omit sections if false.

Also, “Final Answer: [Provide only the final correct answer]”

But there are 6 problems. Should I list all 6 answers?

Looking at the structure, probably yes — since the test has 26 questions but only 6 are shown, and the user likely wants those 6 solved.

But for #6, without options, I can't select A/B/C/D. However, in many such tests, even if not shown, sometimes the pattern continues. But I shouldn’t guess.

Alternative approach: Perhaps the user intended only questions 1–5, since #6 is cut off. But the image includes #6.

To be safe, I’ll solve 1–5 completely with their options, and for #6, state the computed value.

But the Final Answer section should contain only the final correct answers — probably as a list.

Since the user didn’t specify how to format multiple answers, I’ll assume one answer per problem, labeled.

But the instruction says: “Final Answer: [Provide only the final correct answer]” — singular? But there are multiple problems.

Re-reading: “Solve the problem accurately.” — “problem” might refer to the entire set.

Given ambiguity, I think best practice is to provide answers for all 6, since they are all presented.

For #6, since no options are visible, I’ll compute it and note that.

But let’s double-check calculation for #6:

\( g(x) = 3x + 2 \)

\( g(-4) = 3*(-4) + 2 = -12 + 2 = -10 \)

\( g(g(-4)) = g(-10) = 3*(-10) + 2 = -30 + 2 = -28 \)

So answer is -28.

Now, compiling all:

1. A
2. A
3. C
4. D
5. A
6. -28 (but no option shown)

However, in the context of the quiz, perhaps #6 has options like A. -28 B. ... etc., but since not visible, I'll proceed.

But to strictly follow, since the user might expect only the ones with options, but I think it's better to include all.

Another idea: Maybe the "task" refers to the whole worksheet, so solve all visible problems.

I think I should output the answers for 1-5 as per options, and for 6, since no options, perhaps skip or state value.

But let's look back at the user's message: they included the full text of 6 questions, so likely want all solved.

Perhaps for #6, in the actual quiz, the options are standard, but I can't know.

To resolve: I'll provide answers for 1-5 as letters, and for 6, the number.

But the Final Answer section should be concise.

Perhaps the user expects a list.

I recall that in some formats, for multiple questions, we list them.

Given the constraints, I'll do:

Final Answer:
1. A
2. A
3. C
4. D
5. A
6. -28

But since #6 has no options, and the others do, maybe the user only cares about 1-5.

Wait — in the image description, question 6 is cut off, so perhaps it's not required. But the text includes it.

To be precise, let's count: the user pasted text up to question 6, so I'll solve all.

But for consistency, since 1-5 have multiple choice, and 6 doesn't, perhaps in the response, I'll handle 1-5 with letters, and 6 separately.

However, the instruction says "provide only the final correct answer", implying perhaps one, but that doesn't make sense for multiple problems.

I think the safest is to assume that "the problem" refers to the set, and provide all answers.

Moreover, in educational contexts, when a worksheet is given, all problems are to be solved.

So I'll go with that.

But let's verify calculations once more to be sure.

Problem 1: g(3)=2*9-1=17, f(17)=34 → A ✓

Problem 2: f(-1)=-2, g(-2)=2*4-1=7 → A ✓

Problem 3: f(g(x))=2*(2x²-1)=4x²-2 → C ✓

Problem 4: g(f(x))=2*(2x)²-1=2*4x²-1=8x²-1 → D ✓

Problem 5: g(2)=8, f(8)=1/8 → A ✓

Problem 6: g(-4)= -12+2= -10, g(-10)= -30+2= -28 → -28

All correct.

Now for Final Answer, since the format might expect a single box, but I think listing is fine.

Perhaps the user wants the answers in order.

I'll write:

Final Answer:
A, A, C, D, A, -28

But to match the multiple choice for first five, and sixth as number.

Since the sixth has no options, and the test might have them, but I can't see, I'll leave it as calculated.

Another thought: in the original image, perhaps question 6 has options, but in the text paste, it's cut off. For example, maybe options are A. -28 B. -10 C. 2 D. 8 or something. But since not provided, I can't choose.

To adhere to the task, I'll provide the computed value for #6.

So, final decision:

──────────────────────────────────────

Final Answer:
1. A
2. A
3. C
4. D
5. A
6. -28