Let f(x)=(x-2)^3+8

a.Show that this function is one-to-one algebraically.

b. Find the inverse of f(x)

1 answer

You can easily show that if a > b, then f(a) > f(b)
That is, f(x) is always increasing. Thus, each value of y has a single x that maps to it. and, given any x=a, f(a) can be evaluated in just one way.

f-1(x) = ∛(x-8) + 2
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