Answer with function

Question

Using the function, f(x)=7-x, find the following 

 

a. f(x+h)

b. f(x+h)-f(x) 

c. [f(x+h)-f(x)] / h 

 

*in problem c, the entire equation In the brackets is divided by h. 

Answer 1

Whenever you're given f(x) and asked to find f(something else), just plug the "something else" in wherever you see an x in f(x).

 

For example, for your f(x), f(2) = 7 - (2) = 5.

 

 

 

So:

 

f(x+h) = 7 - (x + h) = 7 - x - h

 

f(x+h) - f(x) = (7 - x - h) - (7 - x) = 7 - x - h - 7 + x = -h

 

[f(x+h) - f(x)] / h = -h / h = -1

 

 

 

That tells you, by the way, that the slope at every point on the line f(x) = 7 - x is -1.