Question

Let f and g are two real functions defined as
$f\left(x\right)=2x-3$
$g\left(x\right)=\frac{3+x}{2}$. Find gof and fog.

• A. $f_{o}g=1$ , $g_{o}f=x$
• B. $f_{o}g=2x$ , $g_{o}f=x$
• C. $f_{o}g=x$ , $g_{o}f=x$
• D. $f_{o}g=1$ , $g_{o}f=2x$

Answer 1

Answer: (C)

$f_{o}g=x$ , $g_{o}f=x$

$fog=f\left(g\right(x\left)\right)=f\left(\right(\frac{3+x}{2}\left)\right)=2\left(\right(\frac{3+x}{2}\left)\right)-3=3+x-3=xandgof=g\left(f\right(x\left)\right)g(2x-3)=\left(\right(\frac{3+(2x-3)}{2}\left)\right)=x$