Respuesta :
Answer:
[tex]f(x+h)=\frac{x^2+2xh+h^2}{x+h+3}[/tex] is the answer
given the function [tex]f(x)=\frac{x^2}{x+3}[/tex].
Step-by-step explanation:
[tex]f(x)=\frac{x^2}{x+3}[/tex] 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:
[tex]f(2)=\frac{2^2}{2+3}[/tex]
[tex]f(2)=\frac{4}{5}[/tex]
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:
[tex]f(-2)=\frac{(-2)^2}{(-2)+3}[/tex]
[tex]f(-2)=\frac{4}{1}[/tex]
[tex]f(-2)=4[/tex].
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:
[tex]f(\text{cat+tuna})=\frac{(\text{cat+tuna})^2}{(\text{cat+tuna})+3}[/tex]
[tex]f(\text{cat+tuna})=\frac{(\text{cat+tuna})^2}{\text{cat+tuna}+3}[/tex]
To expand the top, we are going to use this formula for squaring a sum:
[tex](u+v)^2=u^2+2uv+v^2[/tex].
[tex]f(\text{cat+tuna})=\frac{(\text{cat})^2+2\cdot \text{cat} \cdot \text{tuna}+(\text{tuna})^2}{\text{cat+tuna}+3}[/tex]
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:
[tex]f(x+h)=\frac{(x+h)^2}{(x+h)+3}[/tex]
This is really the same problem we had above except without the cat and the tuna but with x and h respectively instead.
[tex]f(x+h)=\frac{x^2+2xh+h^2}{x+h+3}[/tex]
Answer:
Step-by-step 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.
