Questions: Question 8 Find the domain of the function f(x)=8/(x-7) x x<7 x x>7 x x ≠ 7

Solution Steps

The given function is \( f(x) = \frac{8}{x-7} \), which is a rational function. Rational functions are defined for all real numbers except where the denominator is zero.

The denominator of the function is \( x - 7 \). To find where the function is undefined, set the denominator equal to zero:

\[ x - 7 = 0 \]

Solving the equation \( x - 7 = 0 \) gives:

\[ x = 7 \]

This means the function is undefined at \( x = 7 \).

The domain of the function is all real numbers except where the function is undefined. Therefore, the domain is:

\[ \{x \mid x \neq 7\} \]

Final Answer