Function is defined as follows:

Since g(x) is a piecewise function, we need to find the inverse of each piece separately.

The inverse of g(x)=5x2 is x=5g(x)​​.

The inverse of g(x)=21+x is x=g(x)−21.

The inverse of g(x)=2−x​ is x=4−4x​.

Therefore, g−1(7) is equal to $$\begin{align*} \sqrt{\frac{7}{5}} &= \sqrt{\frac{7}{5}} \ 21 + \sqrt{\frac{7}{5}} &= 21 + \sqrt{\frac{7}{5}} \ 4 - 4\sqrt{\frac{7}{5}} &= 4 - 4\sqrt{\frac{7}{5}}. \end{align*}$$ The only solution in the domain of g^{−1}(7) is 4 - 4*sqrt(7/5).

g^-1(7)   does not exist.