Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 12 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · FunctionsYear 12 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) = −4x − 5 and g(x) = 5x + 3. Find f(g(x)) in simplest form.
Answer: −20x − 17
- f(g(x)) = −4(5x + 3) − 5
- = −20x − 17
2.If f(x) = −2x2 − 3x − 8, find f(0).
Answer: −8
- Replace x with 0: −2(0)2 − 3(0) − 8
- = −8
3.f(x) = −4x + 4 and g(x) = x − 1. Find g(f(x)) in simplest form.
Answer: −4x + 3
- g(f(x)) = 1(−4x + 4) − 1
- = −4x + 3
4.f(x) = −4x − 3 and g(x) = −2x − 5. Find f(g(x)) in simplest form.
Answer: 8x + 17
- f(g(x)) = −4(−2x − 5) − 3
- = 8x + 17
5.If f(x) = 2x2 + 6x + 2, find f(3).
Answer: 38
- Replace x with 3: 2(3)2 + 6(3) + 2
- = 38
6.f(x) = −3x − 3 and g(x) = x − 2. Find g(f(x)) in simplest form.
Answer: −3x − 5
- g(f(x)) = 1(−3x − 3) − 2
- = −3x − 5
7.If f(x) = x2 − x + 3, find f(−3).
Answer: 15
- Replace x with −3: (−3)2 − (−3) + 3
- = 15
8.f(x) = 2x − 5 and g(x) = 5x − 4. Find g(f(x)) in simplest form.
Answer: 10x − 29
- g(f(x)) = 5(2x − 5) − 4
- = 10x − 29
9.If f(x) = 3x2 + 5x + 7, find f(−4).
Answer: 35
- Replace x with −4: 3(−4)2 + 5(−4) + 7
- = 35
10.If f(x) = 4x2 − 3x − 5, find f(−3).
Answer: 40
- Replace x with −3: 4(−3)2 − 3(−3) − 5
- = 40
11.f(x) = 2x − 2 and g(x) = 2x − 6. Find f(g(x)) in simplest form.
Answer: 4x − 14
- f(g(x)) = 2(2x − 6) − 2
- = 4x − 14
12.f(x) = −2x − 1 and g(x) = 4x. Find f(g(x)) in simplest form.
Answer: −8x − 1
- f(g(x)) = −2(4x) − 1
- = −8x − 1
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