Question

If f(x) = x^2/x+3, find f(x+h)

Answer 1

Explanation:

You just need to replace all the x's in the equation with (x+h).

So (x+h)^2/(x+h)+3.

I can't tell from the original, but if it is ((x+h)^2) / ((x+h)+3), (over the complete thing) then it can't be simplified and that is the answer.

But if it is ((x+h)^2)/(x+h) + 3, then you can cancel one of the (x+h)'s on the top and get (x+h) + 3 overall.

Answer 2

`f(x+h)=(x^2+2xh+h^2)/(x+h+3)` is the answer

given the function
`f(x)=(x^2)/(x+3)`.

Explanation:

`f(x)=(x^2)/(x+3)` is the given function.

I'm going to do some examples of plugging in because that is what this problem is asking you to do.

Example 1: What is f(2)?

f(2) means we are going to replace x with 2 in the thing we called f:

`f(2)=(2^2)/(2+3)`

`f(2)=(4)/(5)`

Example 2: What is f(-2)?

f(-2) means we are going to replace x with -2 in the thing we called f. Before we do this I just wanted to tell you something here about negative numbers or expressions. When plugging in either of these, use ( ) around the number you are plugging in. So I should re-say my first line here.

f(-2) means we are going to replace x with (-2) in the thing we called f:

`f(-2)=((-2)^2)/((-2)+3)`

`f(-2)=(4)/(1)`

`f(-2)=4`.

Example 3: What is f(cat+tuna)?

f(cat+tuna) means we are going to replace x with (cat+tuna) in the thing we called f:

`f(\text{cat+tuna})=\frac{(\text{cat+tuna})^2}{(\text{cat+tuna})+3}`

`f(\text{cat+tuna})=\frac{(\text{cat+tuna})^2}{\text{cat+tuna}+3}`

To expand the top, we are going to use this formula for squaring a sum:

`(u+v)^2=u^2+2uv+v^2`.

`f(\text{cat+tuna})=\frac{(\text{cat})^2+2\cdot \text{cat} \cdot \text{tuna}+(\text{tuna})^2}{\text{cat+tuna}+3}`

Ok let's move on to the true problem:

f(x+h) means to replace x with (x+h) in the thing we called f:

`f(x+h)=((x+h)^2)/((x+h)+3)`

This is really the same problem we had above except without the cat and the tuna but with x and h respectively instead.

`f(x+h)=(x^2+2xh+h^2)/(x+h+3)`