Find f(a + h) - f(a) for the following function. Simplify your answer. f(x) = x^2 - 10 x + 9

Question

I don't understand how to do this since there is no f(x) to plug in to solve. Just f(a+h) - f(a)

Answer 1

f(x) = x^2 - 10 x + 9

This means that to perform the function, take whatever is inside

the parentheses and square it, then multiply by it by -10 and add that,

then add 9 to that sum:

 

f(a+h) = (a+h)² - 10(a+h) + 9

f(a) = a² -10a + 9

 

f(a+h)-f(a) = (a+h)² - 10(a+h) + 9 - (a² - 10a + 9)

 

= a² + 2ah + h² - 10a - 10h + 9 - a² + 10a - 9

 

Combine like terms for final answer