If f(x) = x^2 -2, then f(x + h)= ? Please explain thoroughly so I can understand how to do these types of problems. Thank you.
This problem requires understanding of the function notation: `f(x) ` means that you take x and plug it into the formula for x.
For example, here `f(x) = x^2 - 2` . So if x = 2 then `f(2) = 2^2 - 2` (= 2). You take x = 2 and plug it into f(x) instead of x and calculate the result.
The same is true when x equals a variable, or a variable expression. For example if x = a, then `f(a) = a^2 - 2` . Replace all x's in the formula for f(x) with a.
In this problem, you need to find `f(x+h)` , so replace all the x's in the formula with x+h:
`f(x+h) = (x+h)^2 - 2` .
Now you still need to simplify this expression by rewriting `(x+h)^2 :`
`(x+h)^2 = (x+h)(x+h) = x^2 + 2xh+h^2`
Finally, `f(x+h) = x^2 + 2xh+h^2 - 2` .