Question

How do you do this problem?

Answer 1

Answer:

2

Step-by-step 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 $\frac{f(x+b)-f(x)}{(x+b)-x}$:

$\frac{f(x+b)-f(x)}{(x+b)-x}=\frac{(2x+2b-1)-(2x-1)}{(x+b)-x}$

                 $=\frac{2x+2b-1-2x+1}{x+b-x}$

                 $=\frac{2b}{b}$   (Cancel common term)

                 $=2$

Hence, $\frac{f(x+b)-f(x)}{(x+b)-x}=2.$