G(x)=x^3 + 1, h(x)=3^x; solve G(h(a))=244

First combine the two functions so that we have an equation for a to solve:

G(h(a)) = (3^x)^3 + 1 = 3^(3x) + 1 = 244

which gives

3^(3x) = 243

Now we can use logarithms in order to solve the equation

log(3^(3x)) = log(243)

but log(3^(3x))=3x*log(3)

so we have x = (log(243))/(3*log(3))

and if we enter this into a calculator we find that x=5/3