For the function g(x)=squareroot(2x+3), find the domain and rage of g.
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The real number domain of x in sqrt(2x+3) is when 2x+3>0 or x>-1.5
Then the range of g(x) is zero to infinity (or all positive real numbers).
To find the domain and range of the function g(x) = √(2x + 3), we need to consider the restrictions on the values of x that make the function defined and any limitations on the outputs.
Domain:
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In this case, since we have a square root function, we must ensure that the expression inside the square root is non-negative.
Let's set 2x + 3 ≥ 0 to find the valid range for x:
2x + 3 ≥ 0
2x ≥ -3
x ≥ -3/2
Therefore, the domain of g(x) is all real numbers greater than or equal to -3/2, or in interval notation: [-3/2, ∞).
Range:
The range of a function represents the set of all the possible output values (y-values) produced by the function. Since we have a square root function, we need to consider the possible values of the expression inside the square root.
Since 2x + 3 can take any non-negative value due to the domain restriction, the square root of it will be a real number (including zero) or undefined. Therefore, we can conclude that the range of g(x) is all real numbers greater than or equal to 0, or [0, ∞).