2011,18, invertible with inverse.

Asked by alanpeter9611 | 26th Feb, 2019, 02:19: AM

Expert Answer:

f(x) = y = x2 + 4
x2 = y - 4
begin mathsize 16px style straight x equals plus-or-minus square root of straight y minus 4 end root end style
f : R+ → [4, ∞)
hence x is positive.
hence we can not take begin mathsize 16px style straight x equals negative square root of straight y minus 4 end root end style
Consider g(y) = begin mathsize 16px style square root of straight y minus 4 end root end style
g : [4, ∞) → R+
Find begin mathsize 16px style straight g ring operator straight f space and space straight f ring operator straight g space we space get space straight g ring operator straight f equals straight I subscript straight x space and space straight f ring operator straight g space equals space straight I subscript straight Y end style
f is invertible.
f-1 = begin mathsize 16px style square root of straight y minus 4 end root end style

Answered by Sneha shidid | 26th Feb, 2019, 09:37: AM