How do you find the inverse of #f(x)=x^2+2x-5# and is it a function?

1 Answer
Ratnaker Mehta
Jul 20, 2016

#f^1# does not exist.

Explanation:

Let us recall that, the inverse of a given function exists, if and only if , the given function is a bijection , i.e., the given function is a 1 - 1 ( one-to-one , or, injection ) and onto ( or, surjection ).

Observe that, for the given function #f#, it is not injective, because,

#f(x)=x^2+2x-5=x(x+2)-5#, so that, #f(0)=-5=f(-2)#, meaning that #f# is an #m-1# or, a #many-to-one# and not a #1-1# function.

Hence, #f^1# does not exist.

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