Determine all the vertical asymptotes of the graph of the function f(x)=(x^2+1)/x^2-1
To determine the vertical asymptotes of the function f(x) = (x^2 + 1) / (x^2 - 1), we need to find the values of x for which the denominator becomes zero.
Setting the denominator, x^2 - 1, equal to zero:
x^2 - 1 = 0
Factoring the quadratic equation:
(x - 1)(x + 1) = 0
Setting each factor equal to zero:
x - 1 = 0 or x + 1 = 0
Solving for x:
x = 1 or x = -1
Therefore, the vertical asymptotes of the function f(x) = (x^2 + 1) / (x^2 - 1) are x = 1 and x = -1.
To determine the vertical asymptotes of the function f(x) = (x^2 + 1)/(x^2 - 1), we need to find the values of x for which the denominator becomes zero.
First, let's set the denominator equal to zero and solve for x:
x^2 - 1 = 0
We can rewrite this equation as:
(x - 1)(x + 1) = 0
Now, setting each factor equal to zero separately, we have:
x - 1 = 0 or x + 1 = 0
Solving these equations, we find:
x = 1 or x = -1
Therefore, the vertical asymptotes of the function f(x) occur at x = 1 and x = -1.