Exercises for Question Type 4: Finding the inverse functions including their domains and range - IB

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Exercises for Question Type 4: Finding the inverse functions including their domains and range - IB

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Question 1

Find the inverse of f (x) = lo g_{2} (5 x - 1), and state the domain and range of f and f^{- 1} .

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Question 2

Find the inverse function of f (x) = (x - 2)^{3} + 1 . Determine the domain and range of f and f^{- 1} .

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Question 3

The question assesses the ability to find the inverse of an exponential function and to identify the domain and range of both the original function and its inverse. This involves logarithmic manipulation and understanding function properties.

Find the inverse of f (x) = e^{x} + 4, and determine the domain and range of f and f^{- 1} .

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Question 4

Find the inverse of f (x) = 3 x - 1, and state the domain and range of f and its inverse.

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Question 5

Find the inverse of f (x) = 4 e^{x} + 32 for 0 < x < 1, and state the domain and range of f and f^{- 1} .

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Question 6

Find the inverse of f (x) = ln (2 x + 3), and give domain and range for both functions.

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Question 7

Given f (x) = x^{2} + 1 with x \geq 0, find f^{- 1} (x) and state domains and ranges.

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Question 8

Find the inverse of f (x) = 2 x - 3 for x \geq \frac{3}{2}, and give all domain and range restrictions.

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Question 9

Find the inverse of f (x) = \frac{x + 1}{x - 2}, stating domain and range of f and f^{- 1} .

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Question 10

Find the inverse of f (x) = \frac{3 x + 5}{2} and give domains and ranges.

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Question 11

Find the inverse function of f (x) = \frac{1}{x + 2}, stating all domain and range restrictions for f and f^{- 1} .

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Question 12

Find the inverse function of f (x) = 5 x - 7 . Determine the domain and range of f and f^{- 1} .

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