Question

If $ f(x)=\frac{2x+1}{3x-2} $ ,then $ fof(2) $ is equal to:

• A. 1
• B. 3
• C. 4
• D. 2

Answer 1

Answer: (D)

Given that $f(x)=\frac{2 x+1}{3 x-2}$
$\therefore fof(x)=f(f(x))$
$=\frac{2\left(\frac{2 x+1}{3 x-2}\right)+1}{3\left(\frac{2 x+1}{3 x-2}\right)-2} $
$=\frac{4 x+2+3 x-2}{6 x+3-6 x+4}=\frac{7 x}{7}=x$
$\Rightarrow fof(2)=2$
Alternate Solution:
Since, $f(x)=\frac{2 x+1}{3 x-2}$
Now, $f(2)=\frac{2 \times 2+1}{3 \times 2-2}=\frac{5}{4}$
$\therefore fof(2)=f(f(2))=f\left(\frac{5}{4}\right)=\frac{2 \times \frac{5}{4}+1}{3 \times \frac{5}{4}-2} $
$=\frac{\frac{10}{4}+1}{\frac{15}{4}-2}=\frac{14}{7}=2$