10th Grade Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the 10th Grade functions worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Functions10th 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) = x2 − 5, find f(0).
Answer: −5
- Replace x with 0: (0)2 − 5
- = −5
2.f(x) = 4x − 2 and g(x) = 5x + 3. Find g(f(x)) in simplest form.
Answer: 20x − 7
- g(f(x)) = 5(4x − 2) + 3
- = 20x − 7
3.f(x) = 2x − 3 and g(x) = 5x + 6. Find g(f(x)) in simplest form.
Answer: 10x − 9
- g(f(x)) = 5(2x − 3) + 6
- = 10x − 9
4.f(x) = x − 5 and g(x) = −3x − 1. Find g(f(x)) in simplest form.
Answer: −3x + 14
- g(f(x)) = −3(x − 5) − 1
- = −3x + 14
5.If f(x) = 3x2 − 6x − 4, find f(0).
Answer: −4
- Replace x with 0: 3(0)2 − 6(0) − 4
- = −4
6.If f(x) = −2x2 − 4x − 9, find f(−2).
Answer: −9
- Replace x with −2: −2(−2)2 − 4(−2) − 9
- = −9
7.f(x) = −2x + 4 and g(x) = x − 3. Find g(f(x)) in simplest form.
Answer: −2x + 1
- g(f(x)) = 1(−2x + 4) − 3
- = −2x + 1
8.If f(x) = −3x2 + 4x − 2, find f(2).
Answer: −6
- Replace x with 2: −3(2)2 + 4(2) − 2
- = −6
9.If f(x) = 2x2 − x − 7, find f(−3).
Answer: 14
- Replace x with −3: 2(−3)2 − (−3) − 7
- = 14
10.If f(x) = 3x2 − 6x + 9, find f(4).
Answer: 33
- Replace x with 4: 3(4)2 − 6(4) + 9
- = 33
11.f(x) = −2x + 3 and g(x) = 5x + 4. Find g(f(x)) in simplest form.
Answer: −10x + 19
- g(f(x)) = 5(−2x + 3) + 4
- = −10x + 19
12.If f(x) = −3x2 − 7, find f(−3).
Answer: −34
- Replace x with −3: −3(−3)2 − 7
- = −34
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