Year 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · FunctionsYear 11 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) = 4x − 1 and g(x) = −4x − 5. Find g(f(x)) in simplest form.
Answer: −16x − 1
- g(f(x)) = −4(4x − 1) − 5
- = −16x − 1
2.f(x) = −2x + 4 and g(x) = −3x − 2. Find g(f(x)) in simplest form.
Answer: 6x − 14
- g(f(x)) = −3(−2x + 4) − 2
- = 6x − 14
3.If f(x) = 3x2 − 2x + 2, find f(4).
Answer: 42
- Replace x with 4: 3(4)2 − 2(4) + 2
- = 42
4.f(x) = 3x − 6 and g(x) = 3x + 1. Find g(f(x)) in simplest form.
Answer: 9x − 17
- g(f(x)) = 3(3x − 6) + 1
- = 9x − 17
5.f(x) = x − 3 and g(x) = 2x − 4. Find f(g(x)) in simplest form.
Answer: 2x − 7
- f(g(x)) = 1(2x − 4) − 3
- = 2x − 7
6.f(x) = x and g(x) = 3x + 3. Find f(g(x)) in simplest form.
Answer: 3x + 3
- f(g(x)) = 1(3x + 3)
- = 3x + 3
7.If f(x) = −2x2 − 6x − 7, find f(2).
Answer: −27
- Replace x with 2: −2(2)2 − 6(2) − 7
- = −27
8.f(x) = 4x + 2 and g(x) = x − 4. Find g(f(x)) in simplest form.
Answer: 4x − 2
- g(f(x)) = 1(4x + 2) − 4
- = 4x − 2
9.If f(x) = −x2 − 3, find f(−4).
Answer: −19
- Replace x with −4: −(−4)2 − 3
- = −19
10.If f(x) = 3x2 + 3, find f(−1).
Answer: 6
- Replace x with −1: 3(−1)2 + 3
- = 6
11.f(x) = −3x − 6 and g(x) = 5x. Find g(f(x)) in simplest form.
Answer: −15x − 30
- g(f(x)) = 5(−3x − 6)
- = −15x − 30
12.If f(x) = −x2 − 2x + 5, find f(5).
Answer: −30
- Replace x with 5: −(5)2 − 2(5) + 5
- = −30
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