Find the domain and range of f(x)=x^2/x^2-9
To find the domain of f(x), we must look for any values of x that would make the denominator equal to zero, since it is undefined to divide by zero. So:
x^2 - 9 = 0
(x + 3)(x - 3) = 0
x = -3 or x = 3
Therefore, the domain of f(x) is all real numbers except -3 and 3, since plugging in these values would result in division by zero.
To find the range of f(x), we can start by seeing what happens as x approaches infinity or negative infinity. As x gets very large in either direction, the x^2 term in the numerator and denominator will dominate, so f(x) will approach 1. Similarly, as x gets very small in either direction, the x^2 term will still dominate, so f(x) will again approach 1. Therefore, the range of f(x) is all real numbers except 1, since f(x) cannot equal 1 due to the excluded values in the domain.