what is the domain function
y=√3x+3
The sqrt sign goes over the 3x+3
can someone show me how to do this problem?
y = √(3x+3)
For x = 2
y = √(3*2 +3) = √9 = 3
Well, let's start with the function y = √(3x + 3). To find the domain of a function, we need to see what values of x the function is defined for.
In this case, the square root function (√) is defined for all non-negative real numbers. So, the expression inside the square root, 3x + 3, must be greater than or equal to zero.
To find the values of x that satisfy this condition, we can set 3x + 3 greater than or equal to zero:
3x + 3 ≥ 0
Now, let's solve for x:
3x ≥ -3
x ≥ -1
So, the domain of the function y = √(3x + 3) is all the real numbers greater than or equal to -1. Written in interval notation, the domain is [-1, ∞).
Now, that wasn't too scary, was it? Mathematics can be fun, just like going to the dentist! Well, maybe not as fun as going to the circus, but close enough!
To find the domain of a function, you need to determine the values of x for which the function is defined. In this case, the function is y = √(3x + 3), where the sqrt symbol is over the entire expression 3x + 3.
To find the domain, you need to consider two factors:
1. The expression inside the square root symbol (3x + 3) must not be negative because you cannot take the square root of a negative number.
2. The expression inside the square root cannot result in division by zero because division by zero is undefined.
Now let's determine the domain step-by-step:
1. Consider the first factor: 3x + 3 ≥ 0.
Subtracting 3 from both sides of the inequality, we get:
3x ≥ -3.
2. Divide both sides of the inequality by 3 to isolate x:
x ≥ -1.
So far, we know that x must be greater than or equal to -1 for the function to be defined.
3. Now, consider the second factor: 3x + 3 ≠ 0.
Subtracting 3 from both sides of the inequality, we get:
3x ≠ -3.
4. Divide both sides of the inequality by 3 to isolate x:
x ≠ -1.
This means that x cannot be equal to -1, as it would result in division by zero.
In summary, the domain of the function y = √(3x + 3) is x ≥ -1, excluding x = -1.
To determine the domain of the function y = √(3x+3), we need to identify the values of x for which the function is defined. The square root function (√) is defined only for non-negative values or zero. In the given function, the expression inside the square root (3x+3) must be greater than or equal to zero for the function to be defined.
To find the domain, we can set the expression inside the square root greater than or equal to zero and solve for x:
3x + 3 ≥ 0
To isolate x, we can subtract 3 from both sides:
3x ≥ -3
Now, divide both sides by 3:
x ≥ -1
This inequality implies that x must be greater than or equal to -1 for the function y = √(3x+3) to be defined.
Therefore, the domain of the function is all real numbers greater than or equal to -1, or in interval notation: [-1, +∞).