Question

$\text{If}f\left(x\right)=2x-1,g\left(x\right)=\frac{x+1}{2},\text{then}fog-gof=$ ___.

• A. 0
• B. 1
• C. can't be found
• D. 2

Answer 1

The correct option is A 0

$\text{Given,}f\left(x\right)=2x-1,g\left(x\right)=\frac{x+1}{2}$
$fog=f\left(g\right(x\left)\right)=f\left(\frac{x+1}{2}\right)=2\left(\frac{x+1}{2}\right)-1=x$

$gof=g\left(f\right(x\left)\right)=g(2x-1)=\left(\frac{2x-1+1}{2}\right)=x$

$\therefore fog-gof=x-x=0$