Question:
If $f: R \rightarrow R$ is defined by $f(x)=x^{2}$, write $f^{-1}(25)$
Solution:
Let $f^{-1}(25)=x \quad \ldots(1)$
$\Rightarrow f(x)=25$
$\Rightarrow x^{2}=25$
$\Rightarrow x^{2}-25=0$
$\Rightarrow(x-5)(x+5)=0$
$\Rightarrow x=\pm 5$
$\Rightarrow f^{-1}(25)=\{-5,5\}$ $[$ from (1)]
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