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

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2 Answers

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”.

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.