The inverse of the function f(x)=1/4x−10 is f^−1 (x)=4x-40. Hence the correct option is b.
To find the inverse of the function f(x)=1/4x−10, we interchange the roles of x and y and solve for the new y. So, let y=f(x):
y=1/4x+10
Now, swap x and y: x=(y-10)4
Solving for y, we get:
y=4x-40
Thus, the inverse function is f^−1 (x)=4x-40. This means that if you apply f^−1 to the output of f or vice versa, you get back to the original input. Hence the correct option is b.