### Home > APCALC > Chapter 1 > Lesson 1.3.1 > Problem1-105

1-105.

Given $f(x) = 2x^2 − 3$:

1. Evaluate $f(2)$.

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

$2(2^²) − 3$

$f(2) = 5$

2. Without writing the equation of the inverse, determine $f ^{-1}(5)$. Explain your process.

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 $f ^{-1}(5)$?

3. Solve for $x$ if $f(x + 2) - f(x - 2) = 64$.

$f(x + 2) = 2((x + 2)^²) - 3 f(x − 2) = 2((x − 2)^²) - 3$

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

Solve for $x$.