Question

Find the inverse of: (x-7)/x with steps

Answer 1

So , Inverse of $f(x) = \frac{x-7}{x}$ is $x = \frac{-7}{y-1}$.

Step-by-step explanation:

An inverse function is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. In functional notation this inverse function would be given by,

${\displaystyle g(y)={\frac {y+7}{5}}}$

With y = 5x − 7 we have that f(x) = y and g(y) = x. Here we have $f(x) = \frac{x-7}{x}$

$f(x) = \frac{x-7}{x}$

⇒ $f(x) = \frac{x-7}{x}$

⇒ $f(x) =1- \frac{7}{x}$

Let f(x) = y:

⇒ $f(x) =1- \frac{7}{x}$

⇒ $y = 1 - \frac{7}{x}$

⇒ $y -1 = \frac{-7}{x}$

⇒ $x = \frac{-7}{y-1}$

So , Inverse of $f(x) = \frac{x-7}{x}$ is $x = \frac{-7}{y-1}$.