Let f : R → R be the function defined by
Question:

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function defined by $f(x)=4 x-3$ for all $x \in \mathbf{R}$. Then write $f^{-1}$.

Solution:

We have,

$f: \mathbf{R} \rightarrow \mathbf{R}$ is the function defined by $f(x)=4 x-3$ for all $x \in \mathbf{R}$

Let $f(x)=y$. Then,

$y=4 x-3$

$\Rightarrow 4 x=y+3$

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

So, $f^{-1}(y)=\frac{y+3}{4}$

or, $f^{-1}(x)=\frac{x+3}{4}$

 

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