solve the function

Question

Given the function
g(x) = 3 − x2,
evaluate
(g(x + h) − g(x))/h    , h ≠ 0.

Answer 1

g(x) = 3-x²

 

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

 

So, g(x+h)-g(x) = -2xh-h²

 

[g(x+h)-g(x)]/h = (-2xh-h²)/h = [h(-2x-h)]/h

 

                                          = -2x-h

Answer 2

I assume you meant 

 

g(x) = 3 - x²

 

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

 

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

 

g(x + h) / h = (-2xh - h²) / h = -2x - h