Find the domain of the following: f(x) = \frac{3}{x-7}

Question:

Find the domain of the following: {eq}f(x) = \frac{3}{x-7} {/eq}

Rational Function:

The domain of a rational function strictly depends on the denominator of the fraction, this is because the denominator has to be different from zero, therefore all the numbers that make the denominator equal to zero will be excluded from the domain.

Function:

{eq}f\left(x\right)=\frac{3}{x-7} {/eq}

The domain is given by the denominator:

{eq}\begin{align*} x-7&=0 \\ x-7+7&=0+7 \\ x&=7 \end{align*} {/eq}

The domain will be: {eq}\left(-\infty \:,\:7\right)\cup \left(7,\:\infty \:\right) {/eq}