Given:
The function is:
[tex]f(x)=\frac{6}{x}[/tex]
Find-:
(A)
The equation of the inverse function
(B)
Graph of f(x) and inverse of f(x)
(C)
Domain and range of f and inverse of f
Explanation-:
The inverse function is defined as a x change for y and y change as x and x slove for y
[tex]\begin{gathered} y=\frac{6}{x} \\ \\ x\Rightarrow y \\ \\ y\Rightarrow x \end{gathered}[/tex]
Solve for "y" then:
[tex]\begin{gathered} y=\frac{6}{x} \\ \\ x\Rightarrow y \\ \\ y\Rightarrow x \\ \\ x=\frac{6}{y} \\ \\ y=\frac{6}{x} \end{gathered}[/tex]
So, the Inverse function is:
[tex]f^{-1}(x)=\frac{6}{x}[/tex]
(B)
The function f(x) and inverse of f(x) are the same then the graph is:
(C)
The domain and range is:
Domain - The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.
[tex]\lbrace x\in\Re:x\ne0\rbrace[/tex]
Range - The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs. In the function machine metaphor, the range is the set of objects that actually come out of the machine when you feed it all the inputs.
[tex]\lbrace y\in\Re:y\ne0\rbrace[/tex]
