Exercises for Question Type 4: Finding inverses for functions that require multiple manipulations

Question 1

Skill question

Find the inverse of $f (x) = \frac{3 x + 5}{2 x - 1}$ .

[4]

Question 2

Skill question

Find the inverse of the function $f (x) = \frac{2 x + 5}{3 x}$ .

[3]

Question 3

Skill question

Find $f^{- 1} (x)$ for $f (x) = \frac{5 x + 7}{2 x - 5}$ .

[3]

Question 4

Skill question

Determine $f^{- 1} (x)$ for $f (x) = \frac{2 x - 3}{x + 4}$ .

[3]

Question 5

Skill question

Compute the inverse of $f (x) = \frac{x - 1}{2 x + 3}$ .

[3]

Question 6

Skill question

Find the inverse function of $f (x) = \frac{4 x + 1}{x - 2}$ .

[3]

Question 7

Skill question

Find an expression for the inverse function $f^{- 1} (x)$ given that $f (x) = \frac{x + 3}{5 x - 2}$ .

[3]

Question 8

Skill question

Let $f (x) = \frac{3 x - 1}{x} + 2$ .

Find an expression for $f^{- 1} (x)$ .

[2]

Question 9

Skill question

Determine $f^{- 1} (x)$ for $f (x) = \frac{1}{x + 2} - 3$ .

[3]

Question 10

Skill question

Determine the inverse of $f (x) = \frac{3 x - 4}{x + 2}$ .

[3]

Question 11

Skill question

Find the inverse of the function $f (x) = \frac{2}{x - 3} + 4$ .

[3]

IB Mathematics Analysis and Approaches Question Type 4: Finding Inverses for Functions That Require Multiple Manipulations Exercises