Year 10 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · FunctionsYear 10 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) = x − 5 and g(x) = −3x − 4. Find g(f(x)) in simplest form.
Answer: −3x + 11
- g(f(x)) = −3(x − 5) − 4
- = −3x + 11
2.If f(x) = −3x2 − 5, find f(−2).
Answer: −17
- Replace x with −2: −3(−2)2 − 5
- = −17
3.If f(x) = −2x2 − 5x − 5, find f(3).
Answer: −38
- Replace x with 3: −2(3)2 − 5(3) − 5
- = −38
4.If f(x) = 2x2 − 3x − 3, find f(1).
Answer: −4
- Replace x with 1: 2(1)2 − 3(1) − 3
- = −4
5.If f(x) = x2 − 3x − 7, find f(−4).
Answer: 21
- Replace x with −4: (−4)2 − 3(−4) − 7
- = 21
6.If f(x) = −x2 − 2x − 1, find f(−2).
Answer: −1
- Replace x with −2: −(−2)2 − 2(−2) − 1
- = −1
7.f(x) = 2x + 3 and g(x) = x − 1. Find g(f(x)) in simplest form.
Answer: 2x + 2
- g(f(x)) = 1(2x + 3) − 1
- = 2x + 2
8.f(x) = −2x + 5 and g(x) = −x + 5. Find g(f(x)) in simplest form.
Answer: 2x
- g(f(x)) = −1(−2x + 5) + 5
- = 2x
9.f(x) = 4x + 6 and g(x) = −3x + 2. Find g(f(x)) in simplest form.
Answer: −12x − 16
- g(f(x)) = −3(4x + 6) + 2
- = −12x − 16
10.f(x) = −x + 2 and g(x) = 5x − 5. Find f(g(x)) in simplest form.
Answer: −5x + 7
- f(g(x)) = −1(5x − 5) + 2
- = −5x + 7
11.If f(x) = −x2 − x − 4, find f(−4).
Answer: −16
- Replace x with −4: −(−4)2 − (−4) − 4
- = −16
12.f(x) = −x − 1 and g(x) = −x + 4. Find f(g(x)) in simplest form.
Answer: x − 5
- f(g(x)) = −1(−x + 4) − 1
- = x − 5
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