Questions: Write the domain in interval notation. (a) f(x)=(x-2)/(x-81) (b) g(x)=(x-2)/(x^2-81) (c) h(x)=(x-2)/(x^2+81)

Solution Steps

The function is $f(x) = \frac{x-2}{x-81}$. The denominator is $x-81$.

Set the denominator equal to zero and solve for x: $x - 81 = 0$ $x = 81$

Since division by zero is undefined, we must exclude $x=81$ from the domain.

The domain is all real numbers except $x=81$. In interval notation, this is $(-\infty, 81) \cup (81, \infty)$.

Final Answer