Let f : R → R be defined as

Question:

Let $f: R \rightarrow R$ be defined as $f(x)=\frac{2 x-3}{4} .$ Write $f o f^{-1}$ (1).

Solution:

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

$\Rightarrow f(y)=x$

$\Rightarrow \frac{2 y-3}{4}=x$

$\Rightarrow 2 y-3=4 x$

$\Rightarrow 2 y=4 x+3$

$\Rightarrow y=\frac{4 x+3}{2}$

$\Rightarrow f^{-1}(x)=\frac{4 x+3}{2} \quad[$ from $(1)]$

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

$\therefore\left(f o f^{-1}\right)(1)=f\left(\frac{4(1)+3}{2}\right)=f\left(\frac{7}{2}\right)=\frac{2\left(\frac{7}{2}\right)-3}{4}=\frac{7-3}{4}=\frac{4}{4}=1$

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