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) = 2x² – 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(x)
f(g(3)) = f(17) = 2*17 = 34

✔ Answer: A. 34

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Problem 2:
If f(x) = 2x and g(x) = 2x² – 1, find g(f(-1))

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

Step 2: Plug that into g(x)
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) = 2x² – 1, find f(g(x))

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

f(g(x)) = f(2x² – 1) = 2*(2x² – 1) = 4x² – 2

✔ Answer: C. 4x² – 2

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Problem 4:
If f(x) = 2x and g(x) = 2x² – 1, find g(f(x))

Plug f(x) into g(x):

g(f(x)) = g(2x) = 2*(2x)² – 1 = 2*(4x²) – 1 = 8x² – 1

✔ Answer: D. 8x² – 1

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Problem 5:
If f(x) = 1/x and g(x) = 3x + 2, find (f g)(2) → which is f(g(2))

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

Step 2: Plug into f(x)
f(8) = 1/8

✔ Answer: A. 1/8

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Problem 6:
If f(x) = 1/x and g(x) = 3x + 2, find (g ∘ g)(-4) → which is g(g(-4))

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

Step 2: Plug that back into g(x)
g(-10) = 3*(-10) + 2 = -30 + 2 = -28

Wait — but looking at the options? The image cuts off after question 6, and no multiple choice options are shown for #6. But since we’re only asked to solve what’s visible, and questions 1–5 have full options, let’s assume we stop here unless told otherwise.

But wait — the user uploaded an image with 6 questions, and question 6 says “find (g g)(-4)” — so we should compute it even if options aren’t visible.

We did:
g(-4) = -10
g(-10) = -28

So answer is -28, but since no options are given in the image for #6, perhaps it's incomplete? However, based on instructions, we must solve accurately.

But hold on — maybe I misread? Let me double-check:

g(x) = 3x + 2
g(-4) = 3*(-4) + 2 = -12 + 2 = -10 ✔️
g(-10) = 3*(-10) + 2 = -30 + 2 = -28 ✔️

So final value is -28

However, since the original image doesn't show answer choices for #6, and our task is to solve the problems as presented, we’ll include it.

But note: In the initial prompt, the user said “Solve the problem accurately” — and there are 6 problems. So we do all 6.

BUT — looking again at the image description: it shows up to question 6, but no answer boxes for #6. Maybe it’s cut off? Still, we calculate it.

Actually — rechecking the user input: they pasted text of the quiz, including question 6, but no options listed for it. That might be an oversight. Since we’re to solve accurately, we provide the computed value.

However, in standardized tests like this, sometimes the last question is incomplete in transcription. But per instruction, we solve what’s given.

Wait — actually, in the original image description provided by user, question 6 ends with “find (g ∘ g)(−4)” and then nothing else — no A/B/C/D. So perhaps it’s a typo or cutoff. But since we’re solving mathematically, we give the correct numerical answer.

But let’s check: maybe I made a mistake?

g(g(-4)) = g(3*(-4)+2) = g(-12+2) = g(-10) = 3*(-10)+2 = -30+2 = -28 ✔️

Yes.

But since the format requires selecting from A/B/C/D when available, and for #6 none are shown, perhaps we skip listing a letter? But the instruction says “solve the problem accurately”, so we state the value.

However, looking back — the user may expect answers only for questions with options. But to be safe, I’ll list all 6 answers numerically, and for #6, since no options, just the number.

But wait — in the response format, we are to put Final Answer section with only the final correct answer — but there are 6 questions! How to handle?

Ah — important: the user uploaded one image with 6 questions. We need to answer all 6.

In such cases, typically we list answers for each.

But the instruction says: “Final Answer: [Provide only the final correct answer]”

That implies one answer? But there are 6 problems.

Re-reading user instruction: “Solve the problem accurately.” — singular? But image has 6.

Looking at context: it’s a quiz with 26 questions, but only first 6 shown. User wants us to solve these 6.

Given that, and since ExplainAnswer etc. are false, we go straight to Final Answer — but how to present 6 answers?

Best approach: Since it’s a multi-question quiz, and no specification, I will list the answers in order.

Also, for #6, since no options, but we calculated -28, and assuming it’s part of the set, we include it.

But let me verify once more all calculations:

1. f(g(3)): g(3)=2*9-1=17; f(17)=34 → A
2. g(f(-1)): f(-1)=-2; g(-2)=2*4-1=7 → A
3. f(g(x))=2*(2x²-1)=4x²-2 → C
4. g(f(x))=2*(2x)^2 -1 = 2*4x² -1 = 8x²-1 → D
5. f(g(2)): g(2)=8; f(8)=1/8 → A
6. g(g(-4)): g(-4)=-10; g(-10)=-28 → ? (no option, but value is -28)

Since the image likely intended to have options for #6 but didn’t display them, and our job is to solve accurately, I’ll report the computed value.

But in many such platforms, if options are missing, perhaps it’s an error. However, per strict interpretation, we output the mathematical result.

Alternatively, maybe I should only answer where options are given? But question 6 is clearly stated.

Another thought: perhaps in the original image, question 6 has options below, but user didn’t paste them. Given that, and to avoid guessing, I’ll provide the calculated answer for #6 as -28.

Now, for Final Answer section — since there are multiple questions, I think the expected format is to list the answers for each.

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

But let’s see the instruction: “Provide only the final correct answer” — singular. Hmm.

Wait — maybe the user considers the entire quiz as one "problem"? Unlikely.

Looking at similar tasks, usually for multi-part, we list all.

To resolve: I’ll assume we need to output answers for all 6, and since #6 has no options, just the number.

But in the interest of matching test format, and since the first five have clear letters, and sixth might be incomplete, but we solved it, I'll include it.

Final decision: List answers as per question numbers.

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