MHT CET · Maths · Functions
If \(f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}\), then the function fof is
- A an even function
- B an identity function
- C a constant function
- D an exponential function
Answer & Solution
Correct Answer
(B) an identity function
Step-by-step Solution
Detailed explanation
(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.
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