11th Grade Function Notation, Composites and Inverses Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the 11th Grade functions worksheet.
Success TutoringWorksheetsAnswer sheet11th Grade · Mathematics · Functions11th 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.If f(x) = 2x2 + 3x + 7, find f(−3).
Answer: 16
- Replace x with −3: 2(−3)2 + 3(−3) + 7
- = 16
2.f(x) = 4x − 5 and g(x) = −4x − 4. Find f(g(x)) in simplest form.
Answer: −16x − 21
- f(g(x)) = 4(−4x − 4) − 5
- = −16x − 21
3.f(x) = 5x − 2 and g(x) = 2x + 6. Find g(f(x)) in simplest form.
Answer: 10x + 2
- g(f(x)) = 2(5x − 2) + 6
- = 10x + 2
4.f(x) = −2x + 1 and g(x) = x − 6. Find f(g(x)) in simplest form.
Answer: −2x + 13
- f(g(x)) = −2(x − 6) + 1
- = −2x + 13
5.f(x) = −x − 6 and g(x) = −x + 3. Find g(f(x)) in simplest form.
Answer: x + 9
- g(f(x)) = −1(−x − 6) + 3
- = x + 9
6.If f(x) = 3x2 + 2x − 1, find f(4).
Answer: 55
- Replace x with 4: 3(4)2 + 2(4) − 1
- = 55
7.f(x) = x − 6 and g(x) = 3x + 6. Find g(f(x)) in simplest form.
Answer: 3x − 12
- g(f(x)) = 3(x − 6) + 6
- = 3x − 12
8.f(x) = −2x − 3 and g(x) = −3x − 5. Find g(f(x)) in simplest form.
Answer: 6x + 4
- g(f(x)) = −3(−2x − 3) − 5
- = 6x + 4
9.If f(x) = −3x2 + 2x + 3, find f(0).
Answer: 3
- Replace x with 0: −3(0)2 + 2(0) + 3
- = 3
10.If f(x) = x2 − 3x + 7, find f(−4).
Answer: 35
- Replace x with −4: (−4)2 − 3(−4) + 7
- = 35
11.If f(x) = −x2 + 5x + 7, find f(−2).
Answer: −7
- Replace x with −2: −(−2)2 + 5(−2) + 7
- = −7
12.If f(x) = −2x2 − x − 9, find f(−4).
Answer: −37
- Replace x with −4: −2(−4)2 − (−4) − 9
- = −37
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