To find the inverse of the function f(x) = ∛(x/7) + 9, we start by replacing f(x) with y:
y = ∛(x/7) + 9
Next, we will isolate x in terms of y. First, subtract 9 from both sides:
y – 9 = ∛(x/7)
Now, to get rid of the cube root, we cube both sides:
(y – 9)³ = x/7
Now, multiply both sides by 7 to solve for x:
x = 7(y – 9)³
Now we have x in terms of y. To express this as the inverse function, we swap x and y:
f-1(x) = 7(x – 9)³
Thus, the inverse function is f-1(x) = 7(x – 9)³.