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 [tex]\frac{f(x+b)-f(x)}{(x+b)-x}[/tex]:
[tex]\frac{f(x+b)-f(x)}{(x+b)-x}=\frac{(2x+2b-1)-(2x-1)}{(x+b)-x}[/tex]
[tex]=\frac{2x+2b-1-2x+1}{x+b-x}[/tex]
[tex]=\frac{2b}{b}[/tex] (Cancel common term)
[tex]=2[/tex]
Hence, [tex]\frac{f(x+b)-f(x)}{(x+b)-x}=2.[/tex]
