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

1-105.
  1. Given f(x) = 2x2 − 3, Homework Help ✎

    1. Evaluate f(2).

    2. Without finding the equation of the inverse, find f −1 (5). Explain your process.

    3. 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.