Exercises for Question Type 5: Finding the inverse of more complex equations and restrictions on the domain

Question 1

Skill question

Find the inverse of $f (x) = \frac{ln ( x ) + 1}{ln ( x ) - 1}$ , for $x > 1$ , $x \neq = e$ .

[5]

Question 2

Skill question

Find $f^{- 1} (x)$ for $f (x) = ln (x^{2} + 1)$ , where $x \geq 0$ .

[3]

Question 3

Skill question

Determine the inverse of $f (x) = \frac{1}{2} ln (5 - 3 x)$ , where $x < \frac{5}{3}$ .

[3]

Question 4

Skill question

Find $f^{- 1} (x)$ if $f (x) = 3 5 ln (\frac{x + 1}{2})$ , for $x > - 1$ .

[3]

Question 5

Skill question

Find $f^{- 1} (x)$ if $f (x) = 5 - ln (2 x)$ , $0 < x \leq \frac{e ^{5}}{2}$ .

[3]

Question 6

Skill question

Determine the inverse of $f (x) = e^{(x + 2)^{3}} - 1$ .

[4]

Question 7

Skill question

Find the inverse of $f (x) = 10 ln (7 x^{3} - 3)$ , where $x \geq (\frac{4}{7})^{1/3}$ .

[5]

Question 8

Skill question

Determine the inverse of $f (x) = ln (5^{x} + 2)$ .

[3]

Question 9

Skill question

Find the inverse of $f (x) = ln (x - 1)$ , for $x > 1$ .

[3]

Question 10

Skill question

Find the inverse of $f (x) = ln ((x - 4)^{4})$ , for $x > 4$ .

[4]

Question 11

Skill question

Determine the inverse of $f (x) = ln (\frac{2 x + 1}{3 - x})$ , for $x < 3$ .

[5]

Question 12

Skill question

Determine the inverse of $f (x) = ln (x)$ , for $x \geq 1$ .

[2]

IB Mathematics Analysis and Approaches Question Type 5: Finding the Inverse of More Complex Equations and Restrictions on the Domain Exercises