Find and Simplify the function

Question

Find and simplify f(a+h)-f(a)/h for the function below

h cannot equal 0

f(x)=2x²-x+1

Answer 1

f(x) = 2x² - x + 1

[f(a+h) - f(a)] / h = [2(a+h)² - (a+h) + 1 - (2a² - a + 1)] / h

= [2(a² + 2ah + h²) - a - h + 1 - 2a² + a - 1] / h = (4ah + 2h² - h) / h = h(4a + 2h - 1) / h = 4a + 2h - 1