Asked by T
Let f(x)=(x-2)^3+8
a.Show that this function is one-to-one algebraically.
b. Find the inverse of f(x)
a.Show that this function is one-to-one algebraically.
b. Find the inverse of f(x)
Answers
Answered by
oobleck
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<sup><sup>-1</sup></sup>(x) = ∛(x-8) + 2
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<sup><sup>-1</sup></sup>(x) = ∛(x-8) + 2
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