Given the function

Question

g(x)=3+2x^2 g^-1(a)? 

Answer 1

The function g(x) = 3 + 2x²

Change g(x) to y.

y = 3 + 2x²

Interchange x and y.

x = 3 + 2y²

Solve for y.

x - 3 = 2y²

y² = (x - 3)/2

Apply square root on each side.

y = ± √[(x - 3)/2]

Change y to g^-1 (x).

g^-1 (x) = ± √[(x - 3)/2]

g^-1 (a) = ± √[(a - 3)/2].