Question

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

Answer 1

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

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)=(-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\\e-3,1\rbrace \end{gathered}`