The inverse of f(x)=3x+1 is [tex]f^{-1} (x) = \frac{1}{3} x-\frac{1}{3}[/tex] which is correct option(c).
What is inverse function?
The inverse function is defined as a function obtained by reversing the given function.
In order to find the inverse of a function, all you have to do is switch where x and y are and resolve for y.
So after switching x and y,
y=3x+1
becomes
x=3y+1
Now, we solve for y regularly.
[tex]3y=x-1[/tex]
[tex]y = \frac{1}{3} (x-{1})[/tex]
[tex]y = \frac{1}{3} x-\frac{1}{3}[/tex]
[tex]f^{-1} (x) = \frac{1}{3} x-\frac{1}{3}[/tex]
Hence, The inverse of f(x)=3x+1 is [tex]f^{-1} (x) = \frac{1}{3} x-\frac{1}{3}[/tex]
Learn more about inverse function here
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