for a given function, $f(x)$, the inverse is denoted by $f^{-1}(x)$. if $f(x)=\frac{2x + 5}{3x}$, what is…

for a given function, $f(x)$, the inverse is denoted by $f^{-1}(x)$. if $f(x)=\frac{2x + 5}{3x}$, what is $f^{-1}(x)$?\na. $\frac{5}{3x - 2}$\nb. $\frac{3x}{2x + 5}$\nc. $-\frac{2x + 5}{3x}$\nd. $\frac{-3x}{2x + 5}$\ne. $\frac{3x - 2}{5}$

for a given function, $f(x)$, the inverse is denoted by $f^{-1}(x)$. if $f(x)=\frac{2x + 5}{3x}$, what is $f^{-1}(x)$?\na. $\frac{5}{3x - 2}$\nb. $\frac{3x}{2x + 5}$\nc. $-\frac{2x + 5}{3x}$\nd. $\frac{-3x}{2x + 5}$\ne. $\frac{3x - 2}{5}$

Answer

Explanation:

Step1: Let $y = f(x)$

Let $y=\frac{2x + 5}{3x}$.

Step2: Swap $x$ and $y$

We get $x=\frac{2y + 5}{3y}$.

Step3: Solve for $y$

First, cross - multiply: $3xy=2y + 5$. Then, move terms with $y$ to one side: $3xy-2y = 5$. Factor out $y$: $y(3x - 2)=5$. Finally, divide both sides by $3x - 2$ to get $y=\frac{5}{3x - 2}$.

Answer:

A. $\frac{5}{3x - 2}$