Year 13 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 13 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · FunctionsYear 13 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.If f(x) = −2x2 + x + 4, find f(4).
Answer: −24
- Replace x with 4: −2(4)2 + (4) + 4
- = −24
2.f(x) = x + 5 and g(x) = x + 6. Find g(f(x)) in simplest form.
Answer: x + 11
- g(f(x)) = 1(x + 5) + 6
- = x + 11
3.If f(x) = −3x2 − 5x − 1, find f(4).
Answer: −69
- Replace x with 4: −3(4)2 − 5(4) − 1
- = −69
4.f(x) = −4x − 2 and g(x) = 3x − 3. Find f(g(x)) in simplest form.
Answer: −12x + 10
- f(g(x)) = −4(3x − 3) − 2
- = −12x + 10
5.If f(x) = 3x2 − x − 9, find f(−2).
Answer: 5
- Replace x with −2: 3(−2)2 − (−2) − 9
- = 5
6.If f(x) = x2 + 6x − 1, find f(3).
Answer: 26
- Replace x with 3: (3)2 + 6(3) − 1
- = 26
7.f(x) = 4x − 3 and g(x) = −4x − 3. Find g(f(x)) in simplest form.
Answer: −16x + 9
- g(f(x)) = −4(4x − 3) − 3
- = −16x + 9
8.If f(x) = 3x2 − 5x + 9, find f(4).
Answer: 37
- Replace x with 4: 3(4)2 − 5(4) + 9
- = 37
9.If f(x) = 2x2 − 6x + 2, find f(0).
Answer: 2
- Replace x with 0: 2(0)2 − 6(0) + 2
- = 2
10.f(x) = x − 4 and g(x) = −2x + 2. Find f(g(x)) in simplest form.
Answer: −2x − 2
- f(g(x)) = 1(−2x + 2) − 4
- = −2x − 2
11.If f(x) = 2x2 − 4x − 8, find f(3).
Answer: −2
- Replace x with 3: 2(3)2 − 4(3) − 8
- = −2
12.f(x) = 2x − 3 and g(x) = 2x. Find g(f(x)) in simplest form.
Answer: 4x − 6
- g(f(x)) = 2(2x − 3)
- = 4x − 6
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