5 BM-03 Composite Function BM-03 Worksheet-02 | PDF | Mathematical ... - Free Printable

Let’s solve each problem step by step.

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Problem 1:
If \( f(x) = 3x - 5 \) and \( g(x) = x^2 \), find \( (f \circ g)(3) \)

This means: first plug 3 into \( g \), then plug that result into \( f \).

Step 1: Find \( g(3) \)
\( g(3) = 3^2 = 9 \)

Step 2: Plug that into \( f \):
\( f(g(3)) = f(9) = 3(9) - 5 = 27 - 5 = 22 \)

✔ Answer for #1: 22

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Problem 2:
If \( f(x) = -9x - 9 \) and \( g(x) = \sqrt{x - 9} \), find \( (f \circ g)(10) \)

Step 1: Find \( g(10) \)
\( g(10) = \sqrt{10 - 9} = \sqrt{1} = 1 \)

Step 2: Plug into \( f \):
\( f(1) = -9(1) - 9 = -9 - 9 = -18 \)

✔ Answer for #2: -18

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Problem 3:
If \( f(x) = -4x + 2 \) and \( g(x) = \sqrt{x - 8} \), find \( (f \circ g)(12) \)

Step 1: Find \( g(12) \)
\( g(12) = \sqrt{12 - 8} = \sqrt{4} = 2 \)

Step 2: Plug into \( f \):
\( f(2) = -4(2) + 2 = -8 + 2 = -6 \)

✔ Answer for #3: -6

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Problem 4:
If \( f(x) = -3x + 4 \) and \( g(x) = x^2 \), find \( (g \circ f)(-2) \)

This means: first plug -2 into \( f \), then plug that result into \( g \).

Step 1: Find \( f(-2) \)
\( f(-2) = -3(-2) + 4 = 6 + 4 = 10 \)

Step 2: Plug into \( g \):
\( g(10) = 10^2 = 100 \)

✔ Answer for #4: 100

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

Step 1: Find \( f(2) \)
\( f(2) = -2(2) + 1 = -4 + 1 = -3 \)

Step 2: Plug into \( g \):
\( g(-3) = \sqrt{(-3)^2 - 5} = \sqrt{9 - 5} = \sqrt{4} = 2 \)

✔ Answer for #5: 2

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Problem 6:
Given \( f(x) = -9x + 3 \) and \( g(x) = x^4 \), find \( (f \circ g)(x) \)

This means: plug \( g(x) \) into \( f \). So wherever you see “x” in \( f \), replace it with \( g(x) = x^4 \).

So:
\( f(g(x)) = f(x^4) = -9(x^4) + 3 = -9x^4 + 3 \)

✔ Answer for #6: -9x⁴ + 3

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Problem 7:
Given \( f(x) = 2x - 5 \) and \( g(x) = x + 2 \), find \( (f \circ g)(x) \)

Plug \( g(x) \) into \( f \):
\( f(g(x)) = f(x + 2) = 2(x + 2) - 5 = 2x + 4 - 5 = 2x - 1 \)

✔ Answer for #7: 2x - 1

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Final Answer:
1. 22
2. -18
3. -6
4. 100
5. 2
6. -9x⁴ + 3
7. 2x - 1