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Find the value of an inverse function

Question:

Given: function y = f (x) in its domain x >= 1 has inverse function, and

f(x + 3) = x² + 6x + 10, find f^-1(5) = ?

Solution:

f(x + 3) = x² + 6x + 10

let t = x + 3, then x = t - 3

change f(x) to f(t)

f(t) = (t - 3)² + 6(t - 3) + 10

f(t) = t² - 6t + 9 + 6t - 18 + 10

f(t) = t² + 1

change variable t to x

f(x) = x² + 1

y = x² + 1