Given:
The function is:
[tex]f(x)=6x[/tex]
To find:
The inverse of the given function, then draw the graphs of function and its inverse.
Solution:
We have,
[tex]f(x)=6x[/tex]
Step 1: Substitute [tex]f(x)=y[/tex].
[tex]y=6x[/tex]
Step 2: Interchange x and y.
[tex]x=6y[/tex]
Step 3: Isolate variable y.
[tex]\dfrac{x}{6}=y[/tex]
Step 4: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]\dfrac{x}{6}=f^{-1}(x)[/tex]
Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{x}{6}[/tex] and the graphs of these functions are shown below.
Note: The inverse function is [tex]g(x)=f^{-1}(x)[/tex].
