### Home > CALC > Chapter 1 > Lesson 1.3.1 > Problem 1-105

1-105.

Given

*f*(*x*) = 2*x*^{2}− 3, Homework Help ✎Evaluate

*f*(2).Without finding the equation of the inverse, find

*f*^{−1}(5). Explain your process.Solve for

*x*if*f*(*x*+ 2) −*f*(*x*− 2) = 64.

Substitute 2 in for every *x* in the equation.

2(2²) − 3

*f*(2) = 5

Recall that that the inputs and outputs are switched for the inverse of a function.

What was the result you found in part (a)? How can you use that to find *f* ^{−1}(5)?

*f*(*x* + 2) = 2((*x* + 2)²) - 3 *f*(*x* − 2) = 2((*x* − 2)²) - 3

Substitute these formulas into the equation above. [2((*x* + 2)²) − 3] − [2((*x* − 2)²) − 3] = 64

Solve for *x*.