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If F : R → R Defined by F(X) = 3x − 4 is Invertible, Then Write F−1 (X). - Mathematics

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Question

If f : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).

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Solution

\[Let f^{- 1} \left( x \right) = y . . . \left( 1 \right)\]
\[ \Rightarrow f\left( y \right) = x\]
\[ \Rightarrow 3y - 4 = x\]
\[ \Rightarrow 3y = x + 4\]
\[ \Rightarrow y = \frac{x + 4}{3}\]
\[ \Rightarrow f^{- 1} \left( x \right) = \frac{x + 4}{3} [from\left( 1 \right)]\]
\[\]
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Chapter 2: Functions - Exercise 2.5 [Page 73]

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RD Sharma Mathematics [English] Class 12
Chapter 2 Functions
Exercise 2.5 | Q 17 | Page 73

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