The given function is not an inverse function across the domain [3,+∞)
We have given that the functions F(x) and G(x)
We have to determine the functions F(x) and G(x) inverse function across the domain [3,+∞)
For functions to be inverse, it must be true that f( g(x) ) = x and g( f(x) ) = x.
What is the inverse function?
The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by[tex]{\displaystyle f^{-1}.}[/tex]
But for F( G(x) ), we have √( G(x) - 3 ) + 8
[tex]= \sqrt{( (x+8)^2} ( - 3 - 3 ) + 8= \sqrt ( (x+8)^ {- 6} ) + 8[/tex]
This -6 part should be canceled out for functions to work out but we cannot do that, therefore F(x) and G(x) are not inverse.
Therefore the given function is not an inverse function across the domain [3,+∞).
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