SOLUTION: Find the domain of the following function f(x)=the square root of the quantity 2x+5

Question 134220: Find the domain of the following function f(x)=the square root of the quantity 2x+5
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 nonnegative)

Set the inner expression greater than or equal to zero

Subtract 5 from both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

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: [,

)

Notice if we graph , we get
notice how the graph never crosses the line . So this graphically verifies our answer.

and we can see that x must be greater than or equal to in order to lie on the graph

RELATED QUESTIONS
Find the domain for the function f(x) = the quotient of the square root of the quantity x (answered by josgarithmetic)

Given the function f(x)= square root:2x-1. c. find the domain of... (answered by user_dude2008)

find the domain of function f(x) = root 2x - 3 (answered by solver91311,Edwin McCravy)

Find the domain and range of the following function: f(x)= square... (answered by jsmallt9)

What is the domain and range of the function f(x)= square root 8-2x? (answered by timvanswearingen)

Find the domain of the function f(x)=^4 the square root of... (answered by Alan3354)

Find the domain of the given function. F(x)=the square root of... (answered by MathLover1)

Find the domain of the function: f(x)= square root of (2x-8) ...then write your... (answered by jim_thompson5910,stanbon)

FIND THE DOMAIN OF THE FUNCTION. f(x)= square root of... (answered by stanbon)