Find f(x) in fog if g(x)=1/2e^x^2 and fog(x)= e^-2x^2 + 1/2e^x^2 + 1

please help! im so confused!

.. fog(x)
= f ( g(x) )
= f ( (1/2)e^(x^2) )

Let u = (1/2)e^(x^2)
... x^2 = ln(2u)

f(u) = e^(-2*ln(u) ) + (1/2) e^( ln(2u) ) + 1
.... = 1/u^2 + u + 1

It would be e^-2x^2 + x + 1 <-----------

Because...

if you plug g(x) into f(x), then you would simply get fog (x)...
so basically it's what you had to plug into fog(x)

x = 1/2e^x^2 is what you plugged into fog