How do you find the domain of g(x) = (5x) /( x^2 - 7x + 12)?

Jun 21, 2018

$x \in \mathbb{R} , x \ne 3 , 4$

Explanation:

The denominator if f(x) cannot be zero as this would make f(x) undefined, Equating the denominator to zero and solving gives the values that x cannot be.

$\text{solve } {x}^{2} - 7 x + 12 = 0 \Rightarrow \left(x - 3\right) \left(x - 4\right) = 0$

$x = 3 , x = 4 \leftarrow \textcolor{red}{\text{excluded values}}$

$\text{domain is } x \in \mathbb{R} , x \ne 3 , 4$
graph{(5x)/(x^2-7x+12 [-20, 20, -10, 10]}