Composition of a piecewise and non-piecewise function

Question

Say you have 2 functions, one of which being a piecewise function:
$f(x)= x^2+2, x<1$ or $2x^2+2, x>=1$
And the other: $g(x)=x^4+1$
How would you find the $f[g(x))]$? I understand regular function composition, I just don't understand what to do when piecewise functions are involved.

Answer 1

Noting that $x^4$ is always nonnegative, we have

$$g(x) = x^4 + 1 \ge 1$$ for all $x$. So when computing $f(g(x))$, we only have to use one part of the piecewise definition.