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: First, find g(3).
g(3) = 2*(3)² - 1 = 2*9 - 1 = 18 - 1 = 17

Step 2: Now 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: First, find f(-1).
f(-1) = 2*(-1) = -2

Step 2: Now 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: f of g of x → plug g(x) into f(x)

So:
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))

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

So:
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)

(f ∘ g)(2) means 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)

(g ∘ g)(-4) means g(g(-4))

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

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

Wait — but looking at the options? The image doesn’t show options for question 6. But since we’re only to give final answers based on what’s visible, and question 6 is incomplete in the image (no options shown), we’ll just compute it correctly.

But since the user didn’t provide options for Q6, and our job is to answer based on the image, perhaps we skip or note it’s incomplete. However, the instruction says “solve the problem accurately” — so we’ll compute it.

Final computed value: -28

But since no options are given, and the quiz likely expects a multiple choice, maybe it’s a typo or cut off. For now, we’ll leave it as calculated.

Actually — rechecking the image: Question 6 is fully written but no options are visible below it. So we can’t select an option. But since the task is to solve, we’ll state the answer.

However, the response format says: “Provide only the final correct answer — this should come AFTER all explanations and reasoning.” And since there are 6 questions, we need to list all final answers.

But the original request was to solve “the problem” — singular — but there are 6. Since the user uploaded the whole page, we’ll assume they want all 6 solved.

But the response format says “Final Answer: [only the final correct answer]” — implying one answer? That’s confusing.

Looking back: The user said “Solve the problem accurately.” and the image has 6 problems. But the response format says “Final Answer:” singular.

Perhaps we should list all 6 answers in order.

But let’s check the rules again: “If you're solving math or logic problems, verify your answer before writing it in the Final Answer section.”

And: “Final Answer: [Provide only the final correct answer — this should come AFTER all explanations and reasoning.]”

Since there are multiple questions, I think we should list them all.

Alternatively, maybe the user intended only one? But the image shows 6.

To be safe, I’ll provide all 6 answers in the Final Answer section, labeled.

But the format says “only the final correct answer” — perhaps meaning for each? Or collectively?

I think the best approach is to list them as:

Final Answer:
1. A
2. A
3. C
4. D
5. A
6. -28 (but since no options, perhaps omit or note)

Wait — for question 6, since no options are shown, and the quiz might have been cut off, but we calculated -28, we’ll include it.

But let’s double-check Q6:

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

So, final answers:

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

But since the format might expect a single box, perhaps we list them in order.

Alternatively, maybe the user only wants the first one? But that doesn’t make sense.

Given the instructions, I’ll proceed to write the final answers for all 6.

But to match the format strictly, perhaps we write:

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

But let’s see — in the image, question 6 has no options, so maybe it’s not part of the multiple choice. But we still solved it.

I think it’s fine.

Now, compiling everything.

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

Explanation:

We are dealing with function composition: putting one function inside another.

For example, f(g(x)) means: first calculate g(x), then take that result and plug it into f.

Let’s go through each:

1. f(g(3)): First, g(3) = 2*(3)^2 - 1 = 18 - 1 = 17. Then f(17) = 2*17 = 34. → A

2. g(f(-1)): First, f(-1) = 2*(-1) = -2. Then g(-2) = 2*(-2)^2 - 1 = 8 - 1 = 7. → A

3. f(g(x)): g(x) = 2x² - 1, so f of that is 2*(2x² - 1) = 4x² - 2. → C

4. g(f(x)): f(x) = 2x, so g of that is 2*(2x)^2 - 1 = 2*4x² - 1 = 8x² - 1. → D

5. (f ∘ g)(2) = f(g(2)): g(2) = 3*2 + 2 = 8, then f(8) = 1/8. → A

6. (g ∘ g)(-4) = g(g(-4)): g(-4) = 3*(-4) + 2 = -10, then g(-10) = 3*(-10) + 2 = -28.

All calculations verified.

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