Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 2 — 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 2 — 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) = 5x + 1 and g(x) = 4x. Find g(f(x)) in simplest form.
Answer: 20x + 4
- g(f(x)) = 4(5x + 1)
- = 20x + 4
2.If f(x) = 2x2 − 5x − 8, find f(2).
Answer: −10
- Replace x with 2: 2(2)2 − 5(2) − 8
- = −10
3.If f(x) = −2x2 − x − 1, find f(−4).
Answer: −29
- Replace x with −4: −2(−4)2 − (−4) − 1
- = −29
4.If f(x) = 2x2 − 3, find f(4).
Answer: 29
- Replace x with 4: 2(4)2 − 3
- = 29
5.If f(x) = x2 − 5x + 6, find f(−1).
Answer: 12
- Replace x with −1: (−1)2 − 5(−1) + 6
- = 12
6.If f(x) = −3x2 − 2x − 4, find f(0).
Answer: −4
- Replace x with 0: −3(0)2 − 2(0) − 4
- = −4
7.If f(x) = 3x2 + 3, find f(1).
Answer: 6
- Replace x with 1: 3(1)2 + 3
- = 6
8.f(x) = −3x − 6 and g(x) = 4x − 3. Find g(f(x)) in simplest form.
Answer: −12x − 27
- g(f(x)) = 4(−3x − 6) − 3
- = −12x − 27
9.f(x) = x and g(x) = 5x + 6. Find f(g(x)) in simplest form.
Answer: 5x + 6
- f(g(x)) = 1(5x + 6)
- = 5x + 6
10.If f(x) = 4x2 − x, find f(−3).
Answer: 39
- Replace x with −3: 4(−3)2 − (−3)
- = 39
11.If f(x) = −3x2 − x − 6, find f(3).
Answer: −36
- Replace x with 3: −3(3)2 − (3) − 6
- = −36
12.f(x) = 4x + 6 and g(x) = 4x + 1. Find g(f(x)) in simplest form.
Answer: 16x + 25
- g(f(x)) = 4(4x + 6) + 1
- = 16x + 25
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