If f(x)=a-x b-x , f(2) is undefined, and f(3)=5, find a and b. - Vidyadip

Question

If $\mathrm{f}(\mathrm{x})=\frac{a-x}{b-x}, \mathrm{f}(2)$ is undefined, and $\mathrm{f}(3)=5$, find $a$ and $\mathrm{b}$.

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Answer

$f(x)=\frac{a-x}{b-x}$
Given that,
$f(2)$ is undefined
$ b-2=0$
$\therefore b=2 \ldots .(i)$
$f(3)=5$
$\therefore \frac{a-3}{b-3}=5$
$\therefore \frac{a-3}{2-3}=5 \ldots . .[\text { [From (i)] }$
$\therefore a-3=-5$
$\therefore a=-2$
$\therefore a=-2, b=2 $

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