SOLUTION: if f(x)=3-x-x^2 then what is( F(x+h)-f(x-h))/h

Question 822538: if f(x)=3-x-x^2 then what is( F(x+h)-f(x-h))/h
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

In function notation, like f(x), the expression between the parentheses, the "x" in f(x), represents the input to the function.
The whole expression, "f(x)", represents the output from f when the input is x.
When you are given a formula for a function, like f(x) = 3-x-x^2, the expression on the right shows us what the function does with its input as it figures out what the output will be. For this particular function
f(x) = 3-x-x^2
tells us that the function f will subtract the input, x, from a 3 and then subtract the square of the input. The result is the output to the function.

So f(x+h) represents the output from function f when the input is x+h. Since we have the formula for f(x) we can figure out what the output will be:

Note the use of parentheses when substituting in the x+h for the x. This is critical. With them we will, for example, subtract the whole x+h from 3 as we should. Without them, 3 - x+h ..., we would subtract the x but not the h.

Simplifying...

There are no like terms so no more simplifying can be done.

Repeating this for f(x-h):

Now that we have f(x+h) and f(x-h) we can deal with:

Substituting in the expressions we got for f(x+h) and f(x-h):

Again with the parentheses!
Simplifying...

A lot of the numerator cancels out because they are opposites.

Adding like terms:

Factoring out h:

The factors of h cancel:

leaving:

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