SOLUTION: Given that f(x) = x^2 + 2, with a domain of x = [0, ∞), find the following:
(f^-1)(x) = [also give domain of the inverse function]
f(3) =
(f^-1)(-7) =
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Question 1117122: Given that f(x) = x^2 + 2, with a domain of x = [0, ∞), find the following:
(f^-1)(x) = [also give domain of the inverse function]
f(3) =
(f^-1)(-7) =
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
y = x^2 +2
:
interchange the y's and x's and solve for y
:
x = y^2 +2
:
y = square root(x -2)
:
f^(-1) (x) = square root(x -2)
:
domain of f^(-1) (x) is [2, infinity)
:
f(3) = 3^2 +2 = 11
:
f^(-1) (-7) is not defined since the domain of f^(-1) (x) does not include negative numbers
:
Note if negative numbers are allowed then f^(-1) (-7) = i * square root(9) which gives us two answers 3i and -3i, i is the square root(-1)
:
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