How do you find the inverse of $f(x) = | x | - 3$ and is it a function?

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Answer 1 · 2018-04-06T09:30:07

The inverse function of $f$ does not exist.

Assuming that, $f : RR to RR : x to f(x)=|x|-3$ , we find,

$f(-1)=|-1|-3=1-3=-2, and, &,$

$f(1)=|1|-3=-2$ .

$rArr f(-1)=f(1)," but, "-1 != 1$ .

Thus, $f$ is not an injection.

We know that,

$"The inverse function of a given function exists"$

$iff" f is bijective, i.e., injective and surjectvie, both"$ .

Hence, the inverse function of $f$ does not exist.

How do you find the inverse of f(x) = | x | - 3f(x) = | x | - 3 and is it a function?