Year 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · FunctionsYear 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — 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 − 5 and g(x) = −x + 2. Find g(f(x)) in simplest form.
Answer: 4x + 7
- g(f(x)) = −1(−4x − 5) + 2
- = 4x + 7
2.f(x) = −x − 3 and g(x) = 3x. Find f(g(x)) in simplest form.
Answer: −3x − 3
- f(g(x)) = −1(3x) − 3
- = −3x − 3
3.f(x) = −x − 2 and g(x) = 3x − 6. Find g(f(x)) in simplest form.
Answer: −3x − 12
- g(f(x)) = 3(−x − 2) − 6
- = −3x − 12
4.f(x) = x − 5 and g(x) = x − 1. Find g(f(x)) in simplest form.
Answer: x − 6
- g(f(x)) = 1(x − 5) − 1
- = x − 6
5.If f(x) = 2x2 + 3x − 7, find f(−1).
Answer: −8
- Replace x with −1: 2(−1)2 + 3(−1) − 7
- = −8
6.f(x) = 3x + 4 and g(x) = −x − 2. Find f(g(x)) in simplest form.
Answer: −3x − 2
- f(g(x)) = 3(−x − 2) + 4
- = −3x − 2
7.If f(x) = 3x2 − 4x − 4, find f(5).
Answer: 51
- Replace x with 5: 3(5)2 − 4(5) − 4
- = 51
8.f(x) = −4x + 2 and g(x) = 2x + 3. Find f(g(x)) in simplest form.
Answer: −8x − 10
- f(g(x)) = −4(2x + 3) + 2
- = −8x − 10
9.f(x) = −x − 3 and g(x) = 2x − 4. Find f(g(x)) in simplest form.
Answer: −2x + 1
- f(g(x)) = −1(2x − 4) − 3
- = −2x + 1
10.If f(x) = −2x2 + 3x + 1, find f(−3).
Answer: −26
- Replace x with −3: −2(−3)2 + 3(−3) + 1
- = −26
11.f(x) = −2x − 1 and g(x) = −4x − 5. Find f(g(x)) in simplest form.
Answer: 8x + 9
- f(g(x)) = −2(−4x − 5) − 1
- = 8x + 9
12.If f(x) = −x2 − 2x − 6, find f(−3).
Answer: −9
- Replace x with −3: −(−3)2 − 2(−3) − 6
- = −9
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