Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — 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 — 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) = x + 3 and g(x) = 3x + 6. Find g(f(x)) in simplest form.
Answer: 3x + 15
- g(f(x)) = 3(x + 3) + 6
- = 3x + 15
2.If f(x) = 3x2 + 6x + 8, find f(3).
Answer: 53
- Replace x with 3: 3(3)2 + 6(3) + 8
- = 53
3.f(x) = −3x + 3 and g(x) = −4x − 6. Find g(f(x)) in simplest form.
Answer: 12x − 18
- g(f(x)) = −4(−3x + 3) − 6
- = 12x − 18
4.f(x) = −2x + 4 and g(x) = x − 5. Find g(f(x)) in simplest form.
Answer: −2x − 1
- g(f(x)) = 1(−2x + 4) − 5
- = −2x − 1
5.f(x) = x − 5 and g(x) = 5x − 6. Find g(f(x)) in simplest form.
Answer: 5x − 31
- g(f(x)) = 5(x − 5) − 6
- = 5x − 31
6.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
7.If f(x) = −x2 + 5x − 6, find f(0).
Answer: −6
- Replace x with 0: −(0)2 + 5(0) − 6
- = −6
8.If f(x) = −x2 − 2x + 7, find f(−3).
Answer: 4
- Replace x with −3: −(−3)2 − 2(−3) + 7
- = 4
9.If f(x) = 2x2 − x + 3, find f(−3).
Answer: 24
- Replace x with −3: 2(−3)2 − (−3) + 3
- = 24
10.f(x) = 5x − 3 and g(x) = x + 3. Find g(f(x)) in simplest form.
Answer: 5x
- g(f(x)) = 1(5x − 3) + 3
- = 5x
11.f(x) = −4x − 3 and g(x) = 2x + 6. Find f(g(x)) in simplest form.
Answer: −8x − 27
- f(g(x)) = −4(2x + 6) − 3
- = −8x − 27
12.f(x) = −3x − 6 and g(x) = −4x − 2. Find f(g(x)) in simplest form.
Answer: 12x
- f(g(x)) = −3(−4x − 2) − 6
- = 12x
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