Answer:
A. The first choice.
Step-by-step explanation:
[tex] f(x) = x^{-2} [/tex]
Let's rewrite the function in a more familiar way.
[tex] f(x) = \dfrac{1}{x^2} [/tex]
Domain:
We know that a denominator cannot equal zero, so we set the denominator equal to zero to find the values of x that must be excluded from the domain.
x^2 = 0
x = 0
The only value excluded from the domain is x = 0.
The domain is all reals except for zero.
Range:
Now that we know the domain is all real numbers except for 0, we look closely at the denominator.
What happens when you replace x with negative numbers? Since you are squaring x, all denominators will be positive. When you replace x with positive numbers, all denominators will also be positive. For values of x with a large absolute value, for example 1000, -1000, 1,000,000 or -1,000,000, as the absolute value of x increases, f(x) approaches zero. For values of x with a small absolute value, such as 0.0001, -0.0001, -0.00000001, or 0.00000001, as x approaches zero, f(x) approaches positive infinity.
The range is all positive real numbers.
Answer:
Domain: all real numbers except 0.
Range: all positive real numbers.
