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Exercises for Question Type 3: Finding the inverse function of simple functions - IB | RevisionDojo

Question 1

Determine the inverse of $f(x)=\frac{3x-4}{5x+2}\,.$

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Question 2

This question explores the properties of linear fractional functions, specifically the derivation of their inverse functions and the conditions required for them to be one-to-one (invertible).

For the general linear fractional function $f(x) = \frac{px+q}{rx+s}$ , derive a formula for the inverse function $f^{-1}(x)$ .

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State the condition on the constants $p, q, r, s$ for the function $f(x)$ to be invertible.

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Question 3

Find the inverse of $f(x) = \frac{x - 2}{x + 3}$ and state its domain and range.

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Question 4

For $f(x)=\frac{2x+1}{x-k}$ , determine the value of $k$ for which $f$ is its own inverse.

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Question 5

The question asks for a formal derivation and algebraic verification of the inverse function property for a given rational function. It assesses skills in algebraic manipulation and composition of functions.

Given $f(x) = \frac{5x-3}{2x+1}$ , show that $f^{-1}(f(x)) = x$ .

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Question 6

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

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Question 7

Let $f(x)=\frac{x+b}{bx-1}$ where $bx \neq 1$ . Determine all real values of $b$ for which $f$ is its own inverse.

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Question 8

For $f(x)=\frac{3x+7}{x-5}$ ,

(a) Find $f^{-1}(x)$ .

(b) Show that $f\bigl(f^{-1}(x)\bigr)=x$ .

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Question 9

Let $f(x)=\frac{2x-1}{3x+4}$ . Prove that $f\bigl(f^{-1}(x)\bigr)=x$ and $f^{-1}\bigl(f(x)\bigr)=x$ .

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Question 10

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

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Question 11

Given parameters $a, b, c$ , define the function $f(x) = \frac{a}{x-b} + c$ .

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

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Show that $f(f^{-1}(x)) = x$ .

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Question Type 3: Finding the inverse function of simple functions Exercises