Search any question & find its solution
Question:
Answered & Verified by Expert
If $f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}$, then the function fof is
Options:
Solution:
2411 Upvotes
Verified Answer
The correct answer is:
an identity function
(B)
$f \circ f=f(f(x))$
$\begin{aligned}
=& \frac{2 \cdot\left(\frac{2 x+3}{3 x-2}\right)+3}{3 \cdot\left(\frac{2 x+3}{3 x-2}\right)-2}=\frac{\frac{4 x+6}{3 x-2}+3}{\frac{6 x+9}{3 x-2}-2} \\
=& \frac{4 x+6+9 x-6}{6 x+9-6 x+4}=\frac{13 x}{13}=x
\end{aligned}$
Therefore, we can say that the composite function for for given function is an identity function.
$f \circ f=f(f(x))$
$\begin{aligned}
=& \frac{2 \cdot\left(\frac{2 x+3}{3 x-2}\right)+3}{3 \cdot\left(\frac{2 x+3}{3 x-2}\right)-2}=\frac{\frac{4 x+6}{3 x-2}+3}{\frac{6 x+9}{3 x-2}-2} \\
=& \frac{4 x+6+9 x-6}{6 x+9-6 x+4}=\frac{13 x}{13}=x
\end{aligned}$
Therefore, we can say that the composite function for for given function is an identity function.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.