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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) = x
^{2}+ 6x + 10, find f^{-1}(5) = ?

- Solution:
- f(x + 3) = x
^{2}+ 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) = t
^{2}~~- 6t~~+ 9~~+ 6t~~- 18 + 10 - f(t) = t
^{2}+ 1 - change variable t to x
- f(x) = x
^{2}+ 1 - y = x
^{2}+ 1

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