Question

How do you do this problem?

Answer 1

2

Explanation:

Let f(x) = 2x – 1

Substitute (x + b) in place of x.

f(x + b) = 2(x + b) – 1

= 2x + 2x –1

To find
`(f(x+b)-f(x))/((x+b)-x)`:

`(f(x+b)-f(x))/((x+b)-x)=((2x+2b-1)-(2x-1))/((x+b)-x)`

`=(2x+2b-1-2x+1)/(x+b-x)`

`=(2b)/(b)` (Cancel common term)

`=2`

Hence,
`(f(x+b)-f(x))/((x+b)-x)=2.`