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Algebra
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