The function given is f(x) = x^2.
We are asked to find f(x+h) and then simplify the expression for f(x+h)-f(x).
First, find the function f(x+h). Replace 'x' in the function f(x) with the term '(x+h)':
f(x+h) = (x+h)^2.
It means that wherever there is 'x' in the function f(x) = x^2, we put 'x+h' instead.
So, we get f(x+h) = (x+h)^2. This is our first result.
Next, remember that f(x) is simply x^2.
Now, we want to find the expression for f(x+h) - f(x).
So, subtract f(x) from f(x+h):
f(x+h) - f(x) = (x+h)^2 - x^2.
We reach the final step when we simplify the expression (x+h)^2 - x^2:
This can be rewritten as (x^2+2*x*h+h^2) - (x^2) after expanding (h + x)^2 = h^2 + 2*x*h + x^2,
Cancelling the like terms (x^2 from both sides), we get our result:
h*(h + 2*x).
So, the final answer is: f(x+h)= (h + x)^2, f(x) = x^2, and f(x+h) - f(x) simplifies to h*(h + 2*x).