How do you find the inverse of #F(x)= e^x+x^2+1#?

1 Answer
Oct 24, 2015

This function is not one-to-one so it has no inverse.

Explanation:

As #x->-oo#, #e^x->0# and #x^2->+oo#, hence #F(x)->+oo#

As #x->oo#, #e^x->+oo# and #x^2->+oo#, hence #F(x)->+oo#

So for sufficiently large values of #y# there are at least #2# values of #x# such that #F(x) = y#.

In fact, the graph of #F(x)# looks like this:

graph{e^x+x^2+1 [-20.33, 19.67, -5.36, 14.64]}

...similar to a parabola, but with a much steeper right hand side.