Year 10 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 10 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · FunctionsYear 10 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 + 1 and g(x) = −2x + 3. Find f(g(x)) in simplest form.
Answer: −8x + 13
- f(g(x)) = 4(−2x + 3) + 1
- = −8x + 13
2.f(x) = 4x + 6 and g(x) = 3x + 4. Find g(f(x)) in simplest form.
Answer: 12x + 22
- g(f(x)) = 3(4x + 6) + 4
- = 12x + 22
3.If f(x) = −x2 − 1, find f(2).
Answer: −5
- Replace x with 2: −(2)2 − 1
- = −5
4.If f(x) = −3x2 − 3x − 5, find f(3).
Answer: −41
- Replace x with 3: −3(3)2 − 3(3) − 5
- = −41
5.If f(x) = 3x2 − x − 2, find f(−4).
Answer: 50
- Replace x with −4: 3(−4)2 − (−4) − 2
- = 50
6.f(x) = 5x − 1 and g(x) = −2x − 5. Find f(g(x)) in simplest form.
Answer: −10x − 26
- f(g(x)) = 5(−2x − 5) − 1
- = −10x − 26
7.If f(x) = x2 − 4x + 1, find f(1).
Answer: −2
- Replace x with 1: (1)2 − 4(1) + 1
- = −2
8.f(x) = −3x and g(x) = 5x. Find f(g(x)) in simplest form.
Answer: −15x
- f(g(x)) = −3(5x)
- = −15x
9.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
10.If f(x) = x2 − 2x, find f(−4).
Answer: 24
- Replace x with −4: (−4)2 − 2(−4)
- = 24
11.If f(x) = 4x2 + 3x + 6, find f(−1).
Answer: 7
- Replace x with −1: 4(−1)2 + 3(−1) + 6
- = 7
12.f(x) = x + 3 and g(x) = 3x − 3. Find g(f(x)) in simplest form.
Answer: 3x + 6
- g(f(x)) = 3(x + 3) − 3
- = 3x + 6
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