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.If f(x) = 3x2 − x − 9, find f(4).
Answer: 35
- Replace x with 4: 3(4)2 − (4) − 9
- = 35
2.If f(x) = −2x2 + 3x + 2, find f(−2).
Answer: −12
- Replace x with −2: −2(−2)2 + 3(−2) + 2
- = −12
3.If f(x) = −3x2 − 2x + 1, find f(−4).
Answer: −39
- Replace x with −4: −3(−4)2 − 2(−4) + 1
- = −39
4.If f(x) = 3x2 − 6x + 6, find f(−4).
Answer: 78
- Replace x with −4: 3(−4)2 − 6(−4) + 6
- = 78
5.f(x) = −x − 5 and g(x) = x − 2. Find g(f(x)) in simplest form.
Answer: −x − 7
- g(f(x)) = 1(−x − 5) − 2
- = −x − 7
6.If f(x) = 4x2 + 4x + 9, find f(−2).
Answer: 17
- Replace x with −2: 4(−2)2 + 4(−2) + 9
- = 17
7.If f(x) = x2 + x − 8, find f(−4).
Answer: 4
- Replace x with −4: (−4)2 + (−4) − 8
- = 4
8.f(x) = 3x − 2 and g(x) = −2x − 2. Find g(f(x)) in simplest form.
Answer: −6x + 2
- g(f(x)) = −2(3x − 2) − 2
- = −6x + 2
9.f(x) = 5x + 2 and g(x) = −2x + 5. Find f(g(x)) in simplest form.
Answer: −10x + 27
- f(g(x)) = 5(−2x + 5) + 2
- = −10x + 27
10.If f(x) = 3x2 − x − 6, find f(−4).
Answer: 46
- Replace x with −4: 3(−4)2 − (−4) − 6
- = 46
11.f(x) = 3x − 1 and g(x) = 2x + 2. Find f(g(x)) in simplest form.
Answer: 6x + 5
- f(g(x)) = 3(2x + 2) − 1
- = 6x + 5
12.If f(x) = −2x2 + x + 9, find f(−3).
Answer: −12
- Replace x with −3: −2(−3)2 + (−3) + 9
- = −12
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