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.If f(x) = −3x2 − 2x + 2, find f(0).
Answer: 2
- Replace x with 0: −3(0)2 − 2(0) + 2
- = 2
2.If f(x) = 2x2 + 6x − 6, find f(−4).
Answer: 2
- Replace x with −4: 2(−4)2 + 6(−4) − 6
- = 2
3.f(x) = 3x + 5 and g(x) = 4x − 1. Find g(f(x)) in simplest form.
Answer: 12x + 19
- g(f(x)) = 4(3x + 5) − 1
- = 12x + 19
4.If f(x) = 3x2 + 4x − 8, find f(5).
Answer: 87
- Replace x with 5: 3(5)2 + 4(5) − 8
- = 87
5.f(x) = 3x + 3 and g(x) = −4x + 2. Find f(g(x)) in simplest form.
Answer: −12x + 9
- f(g(x)) = 3(−4x + 2) + 3
- = −12x + 9
6.If f(x) = 4x2 + x + 2, find f(4).
Answer: 70
- Replace x with 4: 4(4)2 + (4) + 2
- = 70
7.f(x) = −2x − 4 and g(x) = 4x − 4. Find f(g(x)) in simplest form.
Answer: −8x + 4
- f(g(x)) = −2(4x − 4) − 4
- = −8x + 4
8.If f(x) = x2 + x, find f(1).
Answer: 2
- Replace x with 1: (1)2 + (1)
- = 2
9.f(x) = 4x and g(x) = −2x + 6. Find g(f(x)) in simplest form.
Answer: −8x + 6
- g(f(x)) = −2(4x) + 6
- = −8x + 6
10.f(x) = x and g(x) = −3x + 6. Find g(f(x)) in simplest form.
Answer: −3x + 6
- g(f(x)) = −3(x) + 6
- = −3x + 6
11.f(x) = −2x − 2 and g(x) = 2x − 3. Find g(f(x)) in simplest form.
Answer: −4x − 7
- g(f(x)) = 2(−2x − 2) − 3
- = −4x − 7
12.f(x) = 3x + 1 and g(x) = −3x − 4. Find f(g(x)) in simplest form.
Answer: −9x − 11
- f(g(x)) = 3(−3x − 4) + 1
- = −9x − 11
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