Let f : R R be defined as f(x)= 2x-3 4 . Write fof^ -1 (1). - Vidyadip

Question

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

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Answer

Let $f : R \rightarrow R,$ defined by $\text{f(x)}=\frac{2\text{x}-3}{4}$
$\Rightarrow\ \text{f}^{-1}\frac{(2\text{x}-3)}{4}=\text{x}$
$\Rightarrow\ \text{f}^{-1}(2\text{x})=4\text{x}+3$
$\Rightarrow\ \text{f}^{-1}(\text{x})=\frac{4\text{x}+3}{2}$
Now, $fof^{-1}(x) = f(f^{-1}(x))$
$=\text{f}\Big(\frac{4\text{x}+3}{2}\Big)$
$=\frac{2\big(\frac{4\text{x}+3}{2}\big)-3}{4}$
$\Rightarrow fof^{-1}(x) = x$
$\therefore fof^{-1}(1) = 1$

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