Function g is defined as follows:

g(x)=

1. 5x^2 if x≤-3,

2. 21+x if -3

3. 2-√x if x>10.

This function has an inverse.

what is g^-1 (-7)?

The -7 is not in the exponent

TY ;-;

We see that g^−1(−7) is the value of x such that g(x)=−7. Since −7 lies in the interval (−3,10), we use the second piecewise definition of g(x), which gives −7=21+x. Solving for x, we find x=−28, so g^−1(−7) = -28.

This has been answered in a nearby post.