Find domain if f(x)=sqrt 2x+6

Question

Find domain if f(x)=square root of 2x+6

Answer 1

Explanation: The square root symbol tells us that we can only work with positive numbers because we cannot take the square root of a negative number. We will need to find out where the expression under the radical sign is greater or equal to zero. Write this equation.

Step 1: Write the expression under the radical sign as greater or equal to zero. 2x + 6 > 0

Explanation: Now we are ready to solve this equation in order to find out what the x-values of the domain will be. To do this, we must solve for x. Step 2: Solve for x. 2x + 6 > 0 Subtract 6 from both sides of the inequality. 2x > - 6 Divide both sides by positive 2. x > -3

Explanation: We got x > -3, which tells us that the x-values start at and include -3, and they go until infinity. This is represented by [-3, 8). The reason the -3 has a bracket [ ] is because -3 is included. The infinity sign has and will always have a parenthesis ( ) because there is no specific number to include. Infinity just means it goes on and on forever and there is no specific number to “include”.

Answer 2

For the result of the square root to be a real number, the argument can't be negative.

So in f(x) = √(2x+6), the domain is all x for which 2x + 6 ≥ 0. We can solve it easily as follows:

2x + 6 ≥ 0

2x ≥ -6

x ≥ -3   ←  domain.