Year 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 2 — 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 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) = −x. Find g(f(x)) in simplest form.
Answer: 2x + 3
- g(f(x)) = −1(−2x − 3)
- = 2x + 3
2.f(x) = x + 1 and g(x) = −4x + 6. Find f(g(x)) in simplest form.
Answer: −4x + 7
- f(g(x)) = 1(−4x + 6) + 1
- = −4x + 7
3.If f(x) = 3x2 + 4x − 1, find f(1).
Answer: 6
- Replace x with 1: 3(1)2 + 4(1) − 1
- = 6
4.f(x) = 4x and g(x) = −4x + 1. Find f(g(x)) in simplest form.
Answer: −16x + 4
- f(g(x)) = 4(−4x + 1)
- = −16x + 4
5.If f(x) = 2x2 − 5x + 4, find f(−3).
Answer: 37
- Replace x with −3: 2(−3)2 − 5(−3) + 4
- = 37
6.f(x) = 2x + 4 and g(x) = 5x − 5. Find f(g(x)) in simplest form.
Answer: 10x − 6
- f(g(x)) = 2(5x − 5) + 4
- = 10x − 6
7.f(x) = 4x − 4 and g(x) = −x + 4. Find g(f(x)) in simplest form.
Answer: −4x + 8
- g(f(x)) = −1(4x − 4) + 4
- = −4x + 8
8.If f(x) = 3x2 + x + 3, find f(5).
Answer: 83
- Replace x with 5: 3(5)2 + (5) + 3
- = 83
9.If f(x) = 4x2 − x + 1, find f(3).
Answer: 34
- Replace x with 3: 4(3)2 − (3) + 1
- = 34
10.If f(x) = −2x2 − 2x + 6, find f(3).
Answer: −18
- Replace x with 3: −2(3)2 − 2(3) + 6
- = −18
11.If f(x) = 2x2, find f(−4).
Answer: 32
- Replace x with −4: 2(−4)2
- = 32
12.If f(x) = −2x2 − 4x − 5, find f(5).
Answer: −75
- Replace x with 5: −2(5)2 − 4(5) − 5
- = −75
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