If f(x) = frac{2x+3}{3x-2},x neq frac{2}{3},t | vedclass

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(D) Given $f(x) = \frac{2x+3}{3x-2}$.We need to find $(f \circ f)(x) = f(f(x))$.$(f \circ f)(x) = f\left(\frac{2x+3}{3x-2}\right) = \frac{2\left(\frac

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an odd function

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(D) Given $f(x) = \frac{2x+3}{3x-2}$.We need to find $(f \circ f)(x) = f(f(x))$.$(f \circ f)(x) = f\left(\frac{2x+3}{3x-2}\right) = \frac{2\left(\frac{2x+3}{3x-2}\right) + 3}{3\left(\frac{2x+3}{3x-2}\right) - 2}$.Multiplying the numerator and denominator by $(3x-2)$,we get:$(f \circ f)(x) = \frac{2(2x+3) + 3(3x-2)}{3(2x+3) - 2(3x-2)}$.$(f \circ f)(x) = \frac{4x + 6 + 9x - 6}{6x + 9 - 6x + 4} = \frac{13x}{13} = x$.Since $(f \circ f)(x) = x$,and $g(x) = x$ is an odd function,the result is an odd function.

If $f(x) = \frac{2x+3}{3x-2}$,$x \neq \frac{2}{3}$,then $(f \circ f)(x)$ is:

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