### Home > CALC > Chapter 1 > Lesson 1.2.5 > Problem 1-89

1-89.

If

*f*(*x*) =*x*^{2}+ 5 and*g*(*x*) =*x*+ 3 , find and simplify the expressions below. Homework Help ✎*f*(*g*(*x*))*g*(*f*(*x*))*f*^{−1}(−6)*g*^{−1}(−6)

*f*(*g*(*x*)) = *f*(*x* + 3) = ______________

Refer to hint (a).

Even though *f* ^{−1}(*x*) is the inverse of *f*(*x*), you do not need to find the equation of the inverse. Simply evaluate 6 as the *y*-value and solve for *x*.

6 = *f*(*x*)

6 = *x*^{2} + 5

1 = *x*^{2}*x* = ± 1

Refer to hint (c).