Year 11 Function Notation, Composites and Inverses Worksheet — Level 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 — 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.If f(x) = −3x2 + 3x + 9, find f(4).
Answer: −27
- Replace x with 4: −3(4)2 + 3(4) + 9
- = −27
2.If f(x) = 3x2 − 2x − 5, find f(−4).
Answer: 51
- Replace x with −4: 3(−4)2 − 2(−4) − 5
- = 51
3.If f(x) = 2x2 + 3x + 7, find f(0).
Answer: 7
- Replace x with 0: 2(0)2 + 3(0) + 7
- = 7
4.If f(x) = x2 + 3x + 8, find f(4).
Answer: 36
- Replace x with 4: (4)2 + 3(4) + 8
- = 36
5.If f(x) = 2x2 − 8, find f(5).
Answer: 42
- Replace x with 5: 2(5)2 − 8
- = 42
6.If f(x) = −3x2 − 5x − 6, find f(−1).
Answer: −4
- Replace x with −1: −3(−1)2 − 5(−1) − 6
- = −4
7.If f(x) = −2x2 + 6x + 5, find f(5).
Answer: −15
- Replace x with 5: −2(5)2 + 6(5) + 5
- = −15
8.f(x) = 2x − 6 and g(x) = 2x − 2. Find g(f(x)) in simplest form.
Answer: 4x − 14
- g(f(x)) = 2(2x − 6) − 2
- = 4x − 14
9.If f(x) = −x2 + 4x + 8, find f(2).
Answer: 12
- Replace x with 2: −(2)2 + 4(2) + 8
- = 12
10.If f(x) = −2x2 − 2x + 5, find f(3).
Answer: −19
- Replace x with 3: −2(3)2 − 2(3) + 5
- = −19
11.If f(x) = −3x2 − 5, find f(−1).
Answer: −8
- Replace x with −1: −3(−1)2 − 5
- = −8
12.f(x) = 2x and g(x) = 5x + 6. Find g(f(x)) in simplest form.
Answer: 10x + 6
- g(f(x)) = 5(2x) + 6
- = 10x + 6
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