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) = 2x − 3 and g(x) = 5x + 6. Find f(g(x)) in simplest form.
Answer: 10x + 9
- f(g(x)) = 2(5x + 6) − 3
- = 10x + 9
2.If f(x) = x2 − 6x + 4, find f(5).
Answer: −1
- Replace x with 5: (5)2 − 6(5) + 4
- = −1
3.f(x) = x + 2 and g(x) = x + 5. Find f(g(x)) in simplest form.
Answer: x + 7
- f(g(x)) = 1(x + 5) + 2
- = x + 7
4.If f(x) = −x2 − 3x + 6, find f(−3).
Answer: 6
- Replace x with −3: −(−3)2 − 3(−3) + 6
- = 6
5.If f(x) = 2x2 − 2x + 3, find f(0).
Answer: 3
- Replace x with 0: 2(0)2 − 2(0) + 3
- = 3
6.If f(x) = 4x2 + 2x − 4, find f(1).
Answer: 2
- Replace x with 1: 4(1)2 + 2(1) − 4
- = 2
7.If f(x) = x2 − 5x − 7, find f(−2).
Answer: 7
- Replace x with −2: (−2)2 − 5(−2) − 7
- = 7
8.If f(x) = 4x2 + 4x + 7, find f(5).
Answer: 127
- Replace x with 5: 4(5)2 + 4(5) + 7
- = 127
9.f(x) = −2x + 1 and g(x) = 3x + 2. Find g(f(x)) in simplest form.
Answer: −6x + 5
- g(f(x)) = 3(−2x + 1) + 2
- = −6x + 5
10.If f(x) = −2x2 − 2x − 4, find f(−2).
Answer: −8
- Replace x with −2: −2(−2)2 − 2(−2) − 4
- = −8
11.f(x) = −3x + 5 and g(x) = −x − 5. Find g(f(x)) in simplest form.
Answer: 3x − 10
- g(f(x)) = −1(−3x + 5) − 5
- = 3x − 10
12.f(x) = 4x + 2 and g(x) = 2x + 4. Find f(g(x)) in simplest form.
Answer: 8x + 18
- f(g(x)) = 4(2x + 4) + 2
- = 8x + 18
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