The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6
How to determine the inverse function?
The function is given as:
f(x) = x^2 + 6
Rewrite as:
y = x^2 + 6
Swap x and y
x = y^2 + 6
Subtract 6 from both sides
y^2 = x - 6
Take the square root
[tex]y = \sqrt{x - 6}[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt{x - 6}[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6
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