Assume that f2 3 Assume also that the graph of y fx is sym

Assume that f(2) = -3 Assume also that the graph of y = f(x) is symmetric with respect to the line x = -1. Find another value for the function. Another value for the function is f(square box) = square box.

Solution

Since the function is symmetric about x = -1 therefore there must be another value of x for x < -1 for which f(x) = -3.

Now, f(2) = -3

x_o = -1

So distance of the point x = 2 from x = -1 will be: |x_o - a| = | -1 - 2| = 3

This value y = -3 must be repeated for x < -1 at the same distance from x = -1

therefore another x value for which y = -3 will be: x_o - b = -1 - 3 = -4

Hence another value for the function will be: f(- 4) = -3