Find f^-1(x) if f(x)=(x^2+4)?
1 Answer
Sep 9, 2017
Explanation:
We have:
# f(x) = x^2+4 #
And we seek the inverse function,
My preferred approach is to put:
# y = x^2+4 # ..... [A]
And rearrange to form an explicit relationship
So, from [A] we have:
# x^2 = y-4 #
# :. x = +- sqrt(y-4) #
Thus:
# f^(-1)(x) = +- sqrt(x-4) #
Note that by the formal definition
# f(-1) = f(1) = 5 => f^(-1)(5) = +- 1#