Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — 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 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) = 3x + 4 and g(x) = −4x + 2. Find g(f(x)) in simplest form.
Answer: −12x − 14
- g(f(x)) = −4(3x + 4) + 2
- = −12x − 14
2.f(x) = 4x − 1 and g(x) = −x + 1. Find f(g(x)) in simplest form.
Answer: −4x + 3
- f(g(x)) = 4(−x + 1) − 1
- = −4x + 3
3.f(x) = x + 2 and g(x) = 2x − 6. Find f(g(x)) in simplest form.
Answer: 2x − 4
- f(g(x)) = 1(2x − 6) + 2
- = 2x − 4
4.f(x) = 3x + 1 and g(x) = 2x + 3. Find g(f(x)) in simplest form.
Answer: 6x + 5
- g(f(x)) = 2(3x + 1) + 3
- = 6x + 5
5.If f(x) = 4x2 + x + 7, find f(−1).
Answer: 10
- Replace x with −1: 4(−1)2 + (−1) + 7
- = 10
6.f(x) = 5x + 1 and g(x) = −2x + 6. Find f(g(x)) in simplest form.
Answer: −10x + 31
- f(g(x)) = 5(−2x + 6) + 1
- = −10x + 31
7.f(x) = −4x + 6 and g(x) = x + 5. Find f(g(x)) in simplest form.
Answer: −4x − 14
- f(g(x)) = −4(x + 5) + 6
- = −4x − 14
8.If f(x) = 3x2 + 6x + 7, find f(0).
Answer: 7
- Replace x with 0: 3(0)2 + 6(0) + 7
- = 7
9.f(x) = 5x − 3 and g(x) = 4x + 2. Find f(g(x)) in simplest form.
Answer: 20x + 7
- f(g(x)) = 5(4x + 2) − 3
- = 20x + 7
10.f(x) = −3x − 1 and g(x) = −4x. Find g(f(x)) in simplest form.
Answer: 12x + 4
- g(f(x)) = −4(−3x − 1)
- = 12x + 4
11.f(x) = x − 3 and g(x) = 3x − 4. Find f(g(x)) in simplest form.
Answer: 3x − 7
- f(g(x)) = 1(3x − 4) − 3
- = 3x − 7
12.f(x) = −x + 5 and g(x) = 5x − 6. Find g(f(x)) in simplest form.
Answer: −5x + 19
- g(f(x)) = 5(−x + 5) − 6
- = −5x + 19
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