12th Grade Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — 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 4 — 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) = −3x2 + x − 2, find f(−2).
Answer: −16
- Replace x with −2: −3(−2)2 + (−2) − 2
- = −16
2.If f(x) = 2x2 + 4x + 8, find f(−1).
Answer: 6
- Replace x with −1: 2(−1)2 + 4(−1) + 8
- = 6
3.If f(x) = −2x2 − x − 5, find f(2).
Answer: −15
- Replace x with 2: −2(2)2 − (2) − 5
- = −15
4.f(x) = 3x − 1 and g(x) = 3x. Find g(f(x)) in simplest form.
Answer: 9x − 3
- g(f(x)) = 3(3x − 1)
- = 9x − 3
5.f(x) = x + 5 and g(x) = 2x + 3. Find g(f(x)) in simplest form.
Answer: 2x + 13
- g(f(x)) = 2(x + 5) + 3
- = 2x + 13
6.f(x) = 4x − 3 and g(x) = −x + 2. Find f(g(x)) in simplest form.
Answer: −4x + 5
- f(g(x)) = 4(−x + 2) − 3
- = −4x + 5
7.f(x) = x + 4 and g(x) = 5x + 2. Find f(g(x)) in simplest form.
Answer: 5x + 6
- f(g(x)) = 1(5x + 2) + 4
- = 5x + 6
8.If f(x) = 2x2 + 3x − 5, find f(3).
Answer: 22
- Replace x with 3: 2(3)2 + 3(3) − 5
- = 22
9.If f(x) = −3x2 − 6x − 2, find f(5).
Answer: −107
- Replace x with 5: −3(5)2 − 6(5) − 2
- = −107
10.f(x) = −x − 3 and g(x) = −4x − 2. Find f(g(x)) in simplest form.
Answer: 4x − 1
- f(g(x)) = −1(−4x − 2) − 3
- = 4x − 1
11.f(x) = −x − 4 and g(x) = x + 5. Find f(g(x)) in simplest form.
Answer: −x − 9
- f(g(x)) = −1(x + 5) − 4
- = −x − 9
12.If f(x) = 2x2 + 5x − 5, find f(4).
Answer: 47
- Replace x with 4: 2(4)2 + 5(4) − 5
- = 47
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