Question

Find the inverse function in slope-intercept form (mx+b): f(x)=2x-8

Answer 1

Answer:

$\sf f^{-1}(x) = \dfrac{x}{2}+4$

Step-by-step explanation:

A function is given to us and we need to find the inverse of the function in slope intercept form . The given function is ,

$\sf\implies f(x) = 2x - 8$

Let us assume that y = f(x) , so that ,

$\sf\implies y = 2x - 8$

Now interchange the positions of x and y , we have ,

$\sf \implies x = 2y - 8$

Solve for y in terms of x ,

$\sf \implies 2y = x + 8 \\\\\sf\implies y =\dfrac{x}{2}+4$

This is the inverse of the function in slope intercept form. Now we can replace this y with f-¹(x) , as ,

$\sf \implies \boxed{\pink{\frak{f^{-1}(x) = \dfrac{x}{2}+4}}}$