SOLUTION: Graph the square root function and its inverse. Determine the domain and range of both functions. y=square root 2x-2 I got for the first one domain =x is greater than or equal to

Algebra ->  Rational-functions -> SOLUTION: Graph the square root function and its inverse. Determine the domain and range of both functions. y=square root 2x-2 I got for the first one domain =x is greater than or equal to      Log On


   

Question 188731This question is from textbook saxon algebra 2
: Graph the square root function and its inverse. Determine the domain and range of both functions. y=square root 2x-2
I got for the first one domain =x is greater than or equal to 1
the range is y is greater than or equal to 0
Inverse:1/2x+1
domain=x is greater than or equal to 0
range = y is greater than or equal to 1
Am I correct? This question is from textbook saxon algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the original equation y=sqrt%282x-2%29???


If so, then...


Domain: x%3E=1

Range: y%3E=0



y=sqrt%282x-2%29 Start with the given equation.


x=sqrt%282y-2%29 Swap "x" and "y"


x%5E2=2y-2 Square both sides.


x%5E2%2B2=2y Add 2 to both sides.


%28x%5E2%2B2%29%2F2=y Divide both sides by 2.


%28x%5E2%29%2F2%2B%282%29%2F2=y Break up the fraction


%28x%5E2%29%2F2%2B1=y Reduce


%281%2F2%29x%5E2%2B1=y Rearrange the terms.


y=%281%2F2%29x%5E2%2B1 Rearrange the equation


So the inverse of y=sqrt%282x-2%29 is y=%281%2F2%29x%5E2%2B1


Now just swap the original domain and range to get


Domain: x%3E=0

Range: y%3E=1