SOLUTION: what is inverse of g (x)= square root of 2x-1 Write domain and range of g(x) and g^-1(x) in interval notation Thank you!

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Question 981349: what is inverse of g (x)= square root of 2x-1
Write domain and range of g(x) and g^-1(x) in interval notation
Thank you!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You mean g%28x%29=sqrt%282x-1%29 ?

If y is the inverse expression, then sqrt%282y-1%29=x.

%28sqrt%282y-1%29%29%5E2=x%5E2

2y-1=x%5E2

2y=x%5E2%2B1

y=%281%2F2%29x%5E2%2B1%2F2

highlight%28g%5E-1%28x%29=%281%2F2%29x%5E2%2B1%2F2%29


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Domain and Range are now switched between g%28x%29 and g%5E-1%28x%29.
Domain for g(x) is x%3E=1%2F2; range for g(x) is only non-negative numbers, so g%28x%29%3E=0 range.
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g%5E-1%28x%29 Domain & Range:
domain is x%3E=0, and range y%3E=1%2F2.