Doug C. answered • 09/22/23
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Rewrite with f(x) replaced by u.
y = x7 + 3
Form the inverse function:
Interchange x and y
x = y7 + 3
Solve for y by 1) subtracting 3 from both sides, and 2) taking the 7th root of both sides:
y7 = x - 3
y = (x - 3)1/7
Now you can replace y with f-1(x)
f-1(x) = (x - 3)1/7
Confirm:
desmos.com/calculator/4mywtxfabr
Doug C.
Note that the original function is 1-1 (passes the horizontal line test or is always increasing); that means the original function does have an inverse "function".09/22/23