SOLUTION: Hi, looking for the Domain and the Range of Y= the Squareroot of (X-3) Also looking for the inverse of 4x+7. thank you.

Question 148130: Hi,
looking for the Domain and the Range of Y= the Squareroot of (X-3)
Also looking for the inverse of 4x+7.
thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Remember you cannot take the square root of a negative value. So that means the argument must be greater than or equal to zero (i.e. the argument must be positive)

Set the inner expression greater than or equal to zero

Add 3 to both sides

Combine like terms on the right side

So that means x must be greater than or equal to in order for x to be in the domain

So the domain in set-builder notation is

So here is the domain in interval notation: [3,

)

Now to find the range, we must graph the equation

Graph of

From the graph, we can see that the lowest y-value is . So the range in set-builder notation is

Also the range in interval notation is: [0,

)

Start with the given equation.

Switch x and y.

Subtract 7 from both sides.

Divide both sides by 4.

So the inverse function is

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