Respuesta :
Given data:
The given expression for the function is f(x)= 5/(x+3).
The expression for one-to-one function is,
[tex]\begin{gathered} \frac{5}{x_1+3}=\frac{5}{x_2+3} \\ x_2+3=x_1+3 \\ x_2=x_1 \end{gathered}[/tex]The above expression shows that the given function is one-to-one.
The expressionn for the inverse function is,
[tex]\begin{gathered} y=\frac{5}{x+3} \\ y(x+3)=5 \\ xy+3y=5 \\ xy=(5-3y) \\ x=\frac{5-3y}{y} \end{gathered}[/tex]Replace y by x in the above expression.
[tex]f^{-1}(x)=\frac{5-3x}{x}[/tex]Thus, the given function is one-to-one and the expression for the inverse function is (5-3x)/x .
