The domain of y = f(x) = _ is
(a) R - {0}
(b) R
(c) (-2,1)
(d) (-1.1)​

Answer:

The domain of a function is the set of all possible x values that satisfy the equation. We cannot answer this question without first knowing what the equation for f(x) is.

Step-by-step explanation:

Take for example the function y = f(x) = [tex]x^{2} +3[/tex]. Here, you can plug in literally any value for x and still get our a real number. Thus, the domain of f(x) is (-∞, ∞).

However, if your function is y = f(x) = [tex]\frac{2}{\sqrt{x+3} }[/tex] , not every x value is acceptable. First, we cannot have the denominator (bottom part) of the fraction be zero, because division by zero is undefined. Thus, x = -3 is not an acceptable value for x.

We also cannot take the square root of a negative number. Thus, we have the rule that x + 3 must be greater than or equal to zero.

[tex]x+3 > 0\\\\x > -3\\[/tex]

Normally we would use greater than or equal to zero, but because this is in the denominator, we don't want it to equal zero (and thus x = -3 is not acceptable).

So, the domain of x is (-3, ∞). The parenthesis tell us we do not include the negative three and we do not include infinity. In other words, the domain of x is all numbers greater than -3 but less than infinity.

So, first look at your equation for f(x), then see which values of x don't break the rules of math like division by zero or square roots of negative numbers. Good luck!

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