Given f(x)=2x^2−3 , then evaluate f(x−h)+f(x) divided by h , where h is not equal to 0 .

Question

Given f(x)=2x²-3, then evaluate [f(x−h)+f(x)]÷h, where h is not equal to 0.

Answer 1

I think what you are looking for is (f(x + h) - f(x))/h. You may have switched the signs in the numerator. I will do it out that way. If you truly need to do it the way that you have it written, all you need to do is change the signs and follow the same procedure.

This is solved through simple substitution.

f(x + h) = 2(x + h)² - 3

f(x + h) = 2(x² + 2xh + h²) - 3

f(x + h) = 2x² + 4xh + 2h² - 3

Then,

f(x + h) - f(x) = (2x² + 4xh + 2h² - 3) - (2x² - 3)

f(x + h) - f(x) = 2x² - 2x² + 4xh + 2h² - 3 + 3

f(x + h) - f(x) = 4xh + 2h²

Thus,

(f(x + h) - f(x))/h = (4xh + 2h²)/h

(f(x + h) - f(x))/h = 4x + 2h