Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — 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 3 — 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.If f(x) = −x2 + 3x − 3, find f(−3).
Answer: −21
- Replace x with −3: −(−3)2 + 3(−3) − 3
- = −21
2.If f(x) = −2x2 + 8, find f(−4).
Answer: −24
- Replace x with −4: −2(−4)2 + 8
- = −24
3.f(x) = −4x and g(x) = −2x + 2. Find g(f(x)) in simplest form.
Answer: 8x + 2
- g(f(x)) = −2(−4x) + 2
- = 8x + 2
4.If f(x) = 2x2 − 6x − 7, find f(−3).
Answer: 29
- Replace x with −3: 2(−3)2 − 6(−3) − 7
- = 29
5.If f(x) = −3x2 + 3x + 8, find f(4).
Answer: −28
- Replace x with 4: −3(4)2 + 3(4) + 8
- = −28
6.f(x) = x + 5 and g(x) = 2x + 1. Find g(f(x)) in simplest form.
Answer: 2x + 11
- g(f(x)) = 2(x + 5) + 1
- = 2x + 11
7.f(x) = −3x − 1 and g(x) = x + 6. Find g(f(x)) in simplest form.
Answer: −3x + 5
- g(f(x)) = 1(−3x − 1) + 6
- = −3x + 5
8.If f(x) = x2 − 5x + 7, find f(−4).
Answer: 43
- Replace x with −4: (−4)2 − 5(−4) + 7
- = 43
9.f(x) = 4x and g(x) = −4x − 4. Find f(g(x)) in simplest form.
Answer: −16x − 16
- f(g(x)) = 4(−4x − 4)
- = −16x − 16
10.f(x) = 5x − 6 and g(x) = −3x + 3. Find f(g(x)) in simplest form.
Answer: −15x + 9
- f(g(x)) = 5(−3x + 3) − 6
- = −15x + 9
11.If f(x) = −3x2 + 3x + 2, find f(3).
Answer: −16
- Replace x with 3: −3(3)2 + 3(3) + 2
- = −16
12.If f(x) = −2x2 + 3x + 4, find f(−1).
Answer: −1
- Replace x with −1: −2(−1)2 + 3(−1) + 4
- = −1
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