Rewrite a cdf in terms of $F_x (x)$

Question

X is a continuous random variable with a cdf $F_x (x)$, write an expression for the cdf of $Y=X^4$ in terms of $F_x (x)$.

I am completely failing to see how the given function is not already in the desired terms.

I was considering using what my book calls the cumulative distribution function technique, but as I do not know the distribution of this example I was stumped.

Answer 1

Let $G$ be the cdf of $Y$. Then $G(y)=\mathbb P(Y \leqslant y) = \mathbb P(X^4 \leqslant y)$

If $y < 0$, then $G(y)=0$. If $ y \geqslant 0$, then $G(y)=\mathbb P(-y^{1/4} \leqslant X \leqslant y^{1/4})=F_x(y^{1/4}) - F_x(-y^{1/4})$.