Quizizz test on functions operations and composition with multiple-choice questions.

Let’s solve each problem step by step. We are given functions and asked to compute compositions like `f(g(x))`, `g(f(x))`, or specific values like `f(g(3))`.

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Problem 1:

> If `f(x) = 2x` and `g(x) = 2x² - 1`, find `f(g(3))`

Step 1: First, compute `g(3)`
`g(3) = 2*(3)² - 1 = 2*9 - 1 = 18 - 1 = 17`

Step 2: Now 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) = 2x² - 1`, find `g(f(-1))`

Step 1: Compute `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) = 2x² - 1`, find `f(g(x))`

This is the composition `f ∘ g (x) = f(g(x))`

Step 1: Substitute `g(x)` into `f`:
`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 is `g ∘ f (x) = g(f(x))`

Step 1: Substitute `f(x)` into `g`:
`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)`

This means `f(g(2))`

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

Step 2: Plug into `f`:
`f(g(2)) = 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)`

This means `g(g(-4))`

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

Step 2: Plug into `g` again:
`g(g(-4)) = g(-10) = 3*(-10) + 2 = -30 + 2 = -28`

⚠️ Wait — none of the options are `-28`. Let me check the question again.

Looking back at the image:
> 6. If f(x) = 1/x and g(x) = 3x + 2, find (g ∘ g)(−4)

But in the multiple choices, we have:

A) 1/8
B) 1/4
C) 8
D) 7/2

None of these match `-28`. So either:

- There’s a typo in the question or options, OR
- The question was meant to be `(f ∘ g)(-4)` or `(g ∘ f)(-4)`

Let’s test `(f ∘ g)(-4)` just in case:

`g(-4) = -10`, then `f(-10) = -1/10` → not an option.

What about `(g ∘ f)(-4)`?

`f(-4) = -1/4`, then `g(-1/4) = 3*(-1/4) + 2 = -3/4 + 8/4 = 5/4` → not an option.

Wait — maybe it's a misprint, and they meant `(f ∘ g)(2)` again? But that was problem 5.

Alternatively, perhaps the function definitions were swapped? Let me re-read.

No — the question clearly says:
> 6. If f(x) = 1/x and g(x) = 3x + 2, find (g ∘ g)(−4)

So unless there’s a trick, the correct answer is -28, which is not listed.

But since this is a multiple-choice quiz, and all previous answers matched, perhaps there’s an error in the problem.

However, let me double-check my math:

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

So unless the problem meant something else, none of the options are correct.

But wait — looking closely at the image again, maybe I misread the function for problem 6?

Actually, in the image, problem 6 says:

> 6. If f(x) = 1/x and g(x) = 3x + 2, find (g ∘ g)(−4)

And the options are still A) 1/8, B) 1/4, C) 8, D) 7/2 — which are all positive fractions or integers, none matching -28.

This suggests a possible typo in the question or options.

But since this is a quiz, and assuming we must pick from given options, perhaps the intended question was:

> Find (f ∘ g)(2) — which is problem 5, already answered.

Or maybe:

> Find (g ∘ f)(-4) — which we calculated as 5/4 — not listed.

Alternatively, maybe the function `g(x)` is different? But no, it's clearly written as `3x + 2`.

Another possibility: maybe it’s `(f ∘ f)(-4)`?
`f(-4) = -1/4`, then `f(-1/4) = -4` — not listed.

Or `(g ∘ f)(2)`?
`f(2) = 1/2`, then `g(1/2) = 3*(1/2) + 2 = 3/2 + 4/2 = 7/2` → that’s option D!

Ah! Maybe the question was misprinted, and it should be:

> Find (g ∘ f)(2) instead of `(g ∘ g)(-4)`

Because `(g ∘ f)(2) = g(f(2)) = g(1/2) = 3*(1/2) + 2 = 7/2` → matches D

Given that, and since the other problems are straightforward, it’s likely a typo in the question, and the intended problem was:

> 6. If f(x) = 1/x and g(x) = 3x + 2, find (g ∘ f)(2)

Which gives 7/2

✔ So I’ll go with D) 7/2, assuming a typo.

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## ✔ Final Answers:

1. A) 34
2. A) 7
3. C) 4x² - 2
4. D) 8x² - 1
5. A) 1/8
6. D) 7/2 *(assuming typo: meant (g ∘ f)(2) instead of (g ∘ g)(-4))*