Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 12 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · FunctionsYear 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
f(x) notation means "the value of the function at x". For a composite, substitute the inner function into the outer one. For an inverse, swap x and y and solve for y.
1.f(x) = x + 2 and g(x) = 2x − 4. Find f(g(x)) in simplest form.
Answer: 2x − 2
- f(g(x)) = 1(2x − 4) + 2
- = 2x − 2
2.f(x) = 2x + 2 and g(x) = 3x − 1. Find g(f(x)) in simplest form.
Answer: 6x + 5
- g(f(x)) = 3(2x + 2) − 1
- = 6x + 5
3.If f(x) = 2x2 − x − 1, find f(3).
Answer: 14
- Replace x with 3: 2(3)2 − (3) − 1
- = 14
4.If f(x) = −3x2 + x + 6, find f(4).
Answer: −38
- Replace x with 4: −3(4)2 + (4) + 6
- = −38
5.f(x) = 2x + 4 and g(x) = −3x. Find g(f(x)) in simplest form.
Answer: −6x − 12
- g(f(x)) = −3(2x + 4)
- = −6x − 12
6.If f(x) = x2 + 6x − 7, find f(0).
Answer: −7
- Replace x with 0: (0)2 + 6(0) − 7
- = −7
7.If f(x) = −x2 + 6x + 9, find f(3).
Answer: 18
- Replace x with 3: −(3)2 + 6(3) + 9
- = 18
8.f(x) = 2x + 5 and g(x) = 5x − 6. Find f(g(x)) in simplest form.
Answer: 10x − 7
- f(g(x)) = 2(5x − 6) + 5
- = 10x − 7
9.If f(x) = 2x2 − 3x + 1, find f(0).
Answer: 1
- Replace x with 0: 2(0)2 − 3(0) + 1
- = 1
10.If f(x) = 4x2 + 3x + 9, find f(−1).
Answer: 10
- Replace x with −1: 4(−1)2 + 3(−1) + 9
- = 10
11.If f(x) = −3x2 + 4x − 4, find f(4).
Answer: −36
- Replace x with 4: −3(4)2 + 4(4) − 4
- = −36
12.f(x) = 3x + 2 and g(x) = −2x + 1. Find f(g(x)) in simplest form.
Answer: −6x + 5
- f(g(x)) = 3(−2x + 1) + 2
- = −6x + 5
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