Answer:
[tex]\sf f^{-1}(x) = \dfrac{x}{2}+4[/tex]
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 ,
[tex]\sf\implies f(x) = 2x - 8 [/tex]
Let us assume that y = f(x) , so that ,
[tex]\sf\implies y = 2x - 8 [/tex]
Now interchange the positions of x and y , we have ,
[tex]\sf \implies x = 2y - 8[/tex]
Solve for y in terms of x ,
[tex]\sf \implies 2y = x + 8 \\\\\sf\implies y =\dfrac{x}{2}+4 [/tex]
This is the inverse of the function in slope intercept form. Now we can replace this y with f-¹(x) , as ,
[tex]\sf \implies \boxed{\pink{\frak{f^{-1}(x) = \dfrac{x}{2}+4}}}[/tex]
