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

Question:

If $f: R \rightarrow R$ defined by $f(x)=3 x-4$ is invertible, then write $f^{-1}(x)$.

Solution:

Let $f^{-1}(x)=y$            $\ldots(1)$

$\Rightarrow f(y)=x$

$\Rightarrow 3 y-4=x$

$\Rightarrow 3 y=x+4$

$\Rightarrow y=\frac{x+4}{3}$

$\Rightarrow f^{-1}(x)=\frac{x+4}{3} \quad[$ from (1) $]$

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