Question
Check if the following functions have an inverse function. If yes, find the inverse function.
$f(x)=$
✓
Answer
$f(x)=x+7, x<0$
$
=8-x, x \geq 0
$
We observe from the graph that for two values of $x_1$ say $x_1, x_2$ the values of the function are equal.
i.e. $f\left(x_1\right)=f\left(x_2\right)$
$\therefore \mathrm{f}$ is not one-one (i.e. many-one) function.
$\therefore \mathrm{f}$ does not have inverse.
$
=8-x, x \geq 0
$
We observe from the graph that for two values of $x_1$ say $x_1, x_2$ the values of the function are equal.
i.e. $f\left(x_1\right)=f\left(x_2\right)$
$\therefore \mathrm{f}$ is not one-one (i.e. many-one) function.
$\therefore \mathrm{f}$ does not have inverse.
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