Answer:
They are not inverse functions
Step-by-step explanation:
Given
[tex]f(x) = 5x[/tex]
[tex]f^{-1}(x) = x[/tex]
Required
Determine if both are inverse functions
First calculate the inverse of f(x)
[tex]f(x) = 5x[/tex]
Replace f(x) with y
[tex]y = 5x[/tex]
Swap x and y
[tex]x = 5y[/tex]
Make y the subject
[tex]y = \frac{1}{5}x[/tex]
Replace y with f-1(x)
[tex]f^{-1}(x) = \frac{1}{5}x[/tex]
By comparison:
[tex]f^{-1}(x) = x[/tex] and [tex]f^{-1}(x) = \frac{1}{5}x[/tex] are not the same:
Hence:
[tex]f(x) = 5x[/tex] and [tex]f^{-1}(x) = x[/tex] are not inverse functions
