Year 10 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 2 — 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 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) = 4x and g(x) = −4x. Find g(f(x)) in simplest form.
Answer: −16x
- g(f(x)) = −4(4x)
- = −16x
2.If f(x) = −3x2 − 5x − 6, find f(−1).
Answer: −4
- Replace x with −1: −3(−1)2 − 5(−1) − 6
- = −4
3.If f(x) = x2 − 2x − 5, find f(3).
Answer: −2
- Replace x with 3: (3)2 − 2(3) − 5
- = −2
4.If f(x) = 4x2 − 5x − 2, find f(3).
Answer: 19
- Replace x with 3: 4(3)2 − 5(3) − 2
- = 19
5.If f(x) = −2x2 − x − 5, find f(−4).
Answer: −33
- Replace x with −4: −2(−4)2 − (−4) − 5
- = −33
6.If f(x) = 4x2 − 2x − 4, find f(3).
Answer: 26
- Replace x with 3: 4(3)2 − 2(3) − 4
- = 26
7.f(x) = 4x − 5 and g(x) = 3x. Find f(g(x)) in simplest form.
Answer: 12x − 5
- f(g(x)) = 4(3x) − 5
- = 12x − 5
8.If f(x) = −x2 + 4x − 6, find f(−3).
Answer: −27
- Replace x with −3: −(−3)2 + 4(−3) − 6
- = −27
9.f(x) = 2x and g(x) = −2x − 4. Find g(f(x)) in simplest form.
Answer: −4x − 4
- g(f(x)) = −2(2x) − 4
- = −4x − 4
10.If f(x) = x2 + 6x + 1, find f(2).
Answer: 17
- Replace x with 2: (2)2 + 6(2) + 1
- = 17
11.f(x) = x − 1 and g(x) = −3x − 1. Find g(f(x)) in simplest form.
Answer: −3x + 2
- g(f(x)) = −3(x − 1) − 1
- = −3x + 2
12.f(x) = −4x + 6 and g(x) = −4x − 5. Find g(f(x)) in simplest form.
Answer: 16x − 29
- g(f(x)) = −4(−4x + 6) − 5
- = 16x − 29
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