Question

Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q5

Answer 1

Answer:

$T\text{he domain of H\lparen x\rparen is }\lbrace x\lvert x-3,1\rbrace$

Step-by-step explanation:

The domain of a function is all the set of possible x-values that the function can take. Then, for the given function:

$H\left(x\right)=\frac{-7x^2}{\left(x-1\right)\left(x+3\right)}$

The function is undefined when the denominator is equal to 0, then equalize each factor of the denominator to 0:

$\begin{gathered} x-1=0 \\ x=1 \\ \\ x+3=0 \\ x=-3 \\ \\ \text{ Then, the domain of H\lparen x\rparen is }\lbrace x\lvert x\ne-3,1\rbrace \end{gathered}$