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.