The inverse of the function f(x) is \(f^{-1}(x)=\frac{x-6}{5}\).
What is a inverse function?
The inverse function returns the original value for which a function gave the output. The inverse function of a function f is a function that undoes the operation of f.
For the given situation,
The function is f(x) = 5x + 6
let f(x) = y, then
\(x = f^{-1}(y)\)
Now substitute, \(f^{-1}(y)\) in the place of x,
⇒ \(y=5f^{-1}(y)+6\)
⇒ \(y-6=5f^{-1}(y)\)
⇒ \(f^{-1}(y)=\frac{y-6}{5}\)
Now again interchange the function in terms of x,
⇒ \(f^{-1}(x)=\frac{x-6}{5}\)
Hence we can conclude that the inverse of the function f(x) is \(f^{-1}(x)=\frac{x-6}{5}\).
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