Answer is A.
g(x)=2x-3, this is one to one function , so inverse is going to be a function also.
B. Inverse is not going to be a function, because k(x)= - 9x² has x², so for inverse for every value of x will be two value of y.
C. For f(x)=|x+2| inverse will not be a function, because of absolute value, for inverse for every value of x will be two value of y.
D. w(x) = - 20 is a horizontal line. Inverse is going to be vertical line, for one value of x will be infinite values of y. So it is not going to be a function.