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Given f(x)=x+1; g(x)=√x-2; h(x)=2/x Perform the indicated operations and supply...

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spock11 | Student, Undergraduate | (Level 2) eNoter

Posted May 11, 2012 at 4:15 PM via web

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Given f(x)=x+1; g(x)=√x-2; h(x)=2/x Perform the indicated operations and supply the domain and range of the resulting function:

h^-1

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rcmath | High School Teacher | (Level 1) Associate Educator

Posted May 11, 2012 at 4:28 PM (Answer #1)

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To find the inverse function we write y=2/x and solve for x.

`y=2/x=>xy=2=>x=2/y`

Hence the inverse function is `h^(-1)(x)=2/x`

The domain is D=`(-oo,0)U(0,oo)`

The function can never be equal zero, so R=`(-oo,0)U(0,oo)`

The following graph help explain why the function and its inverse are the same.

 

 

 

 

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