Year 13 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 13 functions worksheet.

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Year 13 Function Notation, Composites and Inverses Worksheet — Level 3 — 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.Find the inverse function of f(x) = 2x + 5.

Answer: f⁻¹(x) =

y = 2x + 5
Swap x and y: x = 2y + 5
Solve for y: y =

2.f(x) = 2x − 2 and g(x) = −3x − 6. Find f(g(x)) in simplest form.

Answer: −6x − 14

f(g(x)) = 2(−3x − 6) − 2
= −6x − 14

3.f(x) = 2x + 4 and g(x) = −2x + 4. Find g(f(x)) in simplest form.

Answer: −4x − 4

g(f(x)) = −2(2x + 4) + 4
= −4x − 4

4.f(x) = 3x + 3 and g(x) = 4x + 5. Find g(f(x)) in simplest form.

Answer: 12x + 17

g(f(x)) = 4(3x + 3) + 5
= 12x + 17

5.Find the inverse function of f(x) = 5x + 9.

Answer: f⁻¹(x) =

y = 5x + 9
Swap x and y: x = 5y + 9
Solve for y: y =

6.f(x) = 5x + 6 and g(x) = x − 3. Find f(g(x)) in simplest form.

Answer: 5x − 9

f(g(x)) = 5(x − 3) + 6
= 5x − 9

7.Find the inverse function of f(x) = 3x + 1.

Answer: f⁻¹(x) =

y = 3x + 1
Swap x and y: x = 3y + 1
Solve for y: y =

8.f(x) = 4x + 3 and g(x) = 5x + 5. Find f(g(x)) in simplest form.

Answer: 20x + 23

f(g(x)) = 4(5x + 5) + 3
= 20x + 23

9.Find the inverse function of f(x) = −6x + 4.

Answer: f⁻¹(x) =

y = −6x + 4
Swap x and y: x = −6y + 4
Solve for y: y =

10.f(x) = −3x − 1 and g(x) = −x + 4. Find g(f(x)) in simplest form.

Answer: 3x + 5

g(f(x)) = −1(−3x − 1) + 4
= 3x + 5

11.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

12.f(x) = −x + 5 and g(x) = −3x − 1. Find f(g(x)) in simplest form.

Answer: 3x + 6

f(g(x)) = −1(−3x − 1) + 5
= 3x + 6

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