Question

F(x)=x^2+3x-5. find and simplify f(x+h)-f(x)

Answer 1

Answer:

$f(x + h) - f(x) = h^2 + 3h - 5$

Step-by-step explanation:

Given

$f(x) = x^2 + 3x - 5$

Required

Find f(x + h) - f(x)

In functions:

$f(x + h) = f(x) + f(h)$

So:

$f(x + h) - f(x) = f(x) + f(h) - f(x)$

Collect Like Terms

$f(x + h) - f(x) = f(x) - f(x)+ f(h)$

$f(x + h) - f(x) = f(h)$

Solving for f(h)

$f(h) = h^2 + 3h - 5$

So:

$f(x + h) - f(x) = h^2 + 3h - 5$