12th Grade Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — 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 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 − 2x + 3, find f(−2).
Answer: 15
- Replace x with −2: 2(−2)2 − 2(−2) + 3
- = 15
2.f(x) = x + 2 and g(x) = −4x + 6. Find f(g(x)) in simplest form.
Answer: −4x + 8
- f(g(x)) = 1(−4x + 6) + 2
- = −4x + 8
3.If f(x) = 2x2 − 2x + 5, find f(−2).
Answer: 17
- Replace x with −2: 2(−2)2 − 2(−2) + 5
- = 17
4.If f(x) = −2x2 + 3x − 7, find f(−1).
Answer: −12
- Replace x with −1: −2(−1)2 + 3(−1) − 7
- = −12
5.f(x) = −x + 5 and g(x) = 3x + 5. Find g(f(x)) in simplest form.
Answer: −3x + 20
- g(f(x)) = 3(−x + 5) + 5
- = −3x + 20
6.f(x) = −2x + 5 and g(x) = 5x. Find f(g(x)) in simplest form.
Answer: −10x + 5
- f(g(x)) = −2(5x) + 5
- = −10x + 5
7.f(x) = −4x + 3 and g(x) = −2x − 2. Find g(f(x)) in simplest form.
Answer: 8x − 8
- g(f(x)) = −2(−4x + 3) − 2
- = 8x − 8
8.If f(x) = 4x2 + 3x − 2, find f(−4).
Answer: 50
- Replace x with −4: 4(−4)2 + 3(−4) − 2
- = 50
9.If f(x) = −2x2 − 3x − 5, find f(3).
Answer: −32
- Replace x with 3: −2(3)2 − 3(3) − 5
- = −32
10.If f(x) = 4x2 + 2x + 2, find f(4).
Answer: 74
- Replace x with 4: 4(4)2 + 2(4) + 2
- = 74
11.If f(x) = 4x2 + 4x − 6, find f(−3).
Answer: 18
- Replace x with −3: 4(−3)2 + 4(−3) − 6
- = 18
12.f(x) = −x and g(x) = −x − 4. Find g(f(x)) in simplest form.
Answer: x − 4
- g(f(x)) = −1(−x) − 4
- = x − 4
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