12th Grade Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 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 — Practice Set 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) = 2x − 1 and g(x) = 5x + 2. Find g(f(x)) in simplest form.
Answer: 10x − 3
- g(f(x)) = 5(2x − 1) + 2
- = 10x − 3
2.If f(x) = −3x2 + x + 2, find f(−4).
Answer: −50
- Replace x with −4: −3(−4)2 + (−4) + 2
- = −50
3.f(x) = x + 3 and g(x) = −3x. Find g(f(x)) in simplest form.
Answer: −3x − 9
- g(f(x)) = −3(x + 3)
- = −3x − 9
4.If f(x) = −x2 + 2x + 1, find f(−4).
Answer: −23
- Replace x with −4: −(−4)2 + 2(−4) + 1
- = −23
5.If f(x) = 3x2 + 3x + 1, find f(−1).
Answer: 1
- Replace x with −1: 3(−1)2 + 3(−1) + 1
- = 1
6.If f(x) = 2x2 + 6x − 6, find f(5).
Answer: 74
- Replace x with 5: 2(5)2 + 6(5) − 6
- = 74
7.f(x) = −x − 3 and g(x) = −2x + 6. Find g(f(x)) in simplest form.
Answer: 2x + 12
- g(f(x)) = −2(−x − 3) + 6
- = 2x + 12
8.If f(x) = 3x2 − 3x + 6, find f(4).
Answer: 42
- Replace x with 4: 3(4)2 − 3(4) + 6
- = 42
9.If f(x) = −3x2 − 4x − 3, find f(5).
Answer: −98
- Replace x with 5: −3(5)2 − 4(5) − 3
- = −98
10.If f(x) = −x2 + 3x + 4, find f(−1).
Answer: 0
- Replace x with −1: −(−1)2 + 3(−1) + 4
- = 0
11.If f(x) = 2x2 + x − 8, find f(3).
Answer: 13
- Replace x with 3: 2(3)2 + (3) − 8
- = 13
12.If f(x) = −3x2 − 2x − 9, find f(4).
Answer: −65
- Replace x with 4: −3(4)2 − 2(4) − 9
- = −65
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