Year 13 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 13 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · FunctionsYear 13 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.f(x) = −4x and g(x) = 5x − 6. Find g(f(x)) in simplest form.
Answer: −20x − 6
- g(f(x)) = 5(−4x) − 6
- = −20x − 6
2.If f(x) = −x2 + 5x − 3, find f(2).
Answer: 3
- Replace x with 2: −(2)2 + 5(2) − 3
- = 3
3.If f(x) = 2x2 + 4x − 2, find f(2).
Answer: 14
- Replace x with 2: 2(2)2 + 4(2) − 2
- = 14
4.f(x) = x + 4 and g(x) = x + 3. Find g(f(x)) in simplest form.
Answer: x + 7
- g(f(x)) = 1(x + 4) + 3
- = x + 7
5.f(x) = 2x + 4 and g(x) = 5x + 3. Find f(g(x)) in simplest form.
Answer: 10x + 10
- f(g(x)) = 2(5x + 3) + 4
- = 10x + 10
6.f(x) = 5x − 2 and g(x) = −4x + 2. Find f(g(x)) in simplest form.
Answer: −20x + 8
- f(g(x)) = 5(−4x + 2) − 2
- = −20x + 8
7.If f(x) = −3x2 − 2, find f(−3).
Answer: −29
- Replace x with −3: −3(−3)2 − 2
- = −29
8.f(x) = −3x + 6 and g(x) = −2x − 3. Find g(f(x)) in simplest form.
Answer: 6x − 15
- g(f(x)) = −2(−3x + 6) − 3
- = 6x − 15
9.f(x) = 2x − 5 and g(x) = 3x − 2. Find g(f(x)) in simplest form.
Answer: 6x − 17
- g(f(x)) = 3(2x − 5) − 2
- = 6x − 17
10.f(x) = 4x − 3 and g(x) = −4x + 6. Find g(f(x)) in simplest form.
Answer: −16x + 18
- g(f(x)) = −4(4x − 3) + 6
- = −16x + 18
11.If f(x) = x2 − 5x + 2, find f(1).
Answer: −2
- Replace x with 1: (1)2 − 5(1) + 2
- = −2
12.If f(x) = 2x2 + 3x + 1, find f(2).
Answer: 15
- Replace x with 2: 2(2)2 + 3(2) + 1
- = 15
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