Given:
Consider the function is
[tex]f(x)=\dfrac{3x+2}{x}[/tex]
To find:
The inverse of the function, .i.e., [tex]f^{-1}(x)[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{3x+2}{x}[/tex]
Putting f(x)=y, we get
[tex]x=\dfrac{3y+2}{y}[/tex]
Isolate the variable y.
[tex]xy=3y+2[/tex]
[tex]xy-3y=2[/tex]
[tex]y(x-3)=2[/tex]
[tex]y=\dfrac{2}{x-3}[/tex]
Putting [tex]y=f^{-1}(x)[/tex], we get
[tex]f^{-1}(x)=\dfrac{2}{x-3}[/tex]
Therefore, the inverse function is [tex]f^{-1}(x)=\dfrac{2}{x-3}[/tex].
