12th Grade Function Notation, Composites and Inverses Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the 12th Grade functions worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Functions12th Grade 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) = 5x + 2 and g(x) = 4x − 5. Find g(f(x)) in simplest form.
Answer: 20x + 3
- g(f(x)) = 4(5x + 2) − 5
- = 20x + 3
2.If f(x) = 2x2 + 4x + 2, find f(3).
Answer: 32
- Replace x with 3: 2(3)2 + 4(3) + 2
- = 32
3.f(x) = −2x − 5 and g(x) = −3x − 4. Find f(g(x)) in simplest form.
Answer: 6x + 3
- f(g(x)) = −2(−3x − 4) − 5
- = 6x + 3
4.If f(x) = x2 − x − 1, find f(−4).
Answer: 19
- Replace x with −4: (−4)2 − (−4) − 1
- = 19
5.If f(x) = −x2 + 5x + 3, find f(5).
Answer: 3
- Replace x with 5: −(5)2 + 5(5) + 3
- = 3
6.If f(x) = 2x2 − 2x − 6, find f(1).
Answer: −6
- Replace x with 1: 2(1)2 − 2(1) − 6
- = −6
7.If f(x) = 2x2 + 4x − 4, find f(3).
Answer: 26
- Replace x with 3: 2(3)2 + 4(3) − 4
- = 26
8.f(x) = 4x − 1 and g(x) = −2x − 3. Find g(f(x)) in simplest form.
Answer: −8x − 1
- g(f(x)) = −2(4x − 1) − 3
- = −8x − 1
9.f(x) = −x + 2 and g(x) = −2x + 1. Find g(f(x)) in simplest form.
Answer: 2x − 3
- g(f(x)) = −2(−x + 2) + 1
- = 2x − 3
10.f(x) = 4x − 5 and g(x) = x. Find f(g(x)) in simplest form.
Answer: 4x − 5
- f(g(x)) = 4(x) − 5
- = 4x − 5
11.f(x) = −2x + 5 and g(x) = −3x − 2. Find g(f(x)) in simplest form.
Answer: 6x − 17
- g(f(x)) = −3(−2x + 5) − 2
- = 6x − 17
12.If f(x) = −3x2 + 6x + 8, find f(−3).
Answer: −37
- Replace x with −3: −3(−3)2 + 6(−3) + 8
- = −37
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