Question
The function \( h \) is defined below. \[ h(x)=\frac{x^{2}+3 x-10}{x^{2}-3 x-40} \] Find all values of \( x \) that are NOT in the domain of \( h \). If there is more than one value, separate them with commas. \( x=\square \)
Ask by Guzman Weaver. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The values of \( x \) not in the domain of \( h \) are \( x=-5,8 \).
Solution
Solve the equation \( x^{2}-3x-40=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}-3x-40=0\)
- step1: Factor the expression:
\(\left(x-8\right)\left(x+5\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-8=0\\&x+5=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=8\\&x=-5\end{align}\)
- step4: Rewrite:
\(x_{1}=-5,x_{2}=8\)
The values of \( x \) that are not in the domain of the function \( h \) are \( x=-5 \) and \( x=8 \). Therefore, the values of \( x \) that are not in the domain of \( h \) are \( x=-5,8 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find the values of \( x \) that are NOT in the domain of \( h(x) \), we must identify where the denominator is equal to zero, since division by zero is undefined. The denominator of \( h(x) \) is given by: \[ x^2 - 3x - 40 \] We set the denominator to zero: \[ x^2 - 3x - 40 = 0 \] Next, we can factor the quadratic: \[ (x - 8)(x + 5) = 0 \] Setting each factor equal to zero gives us: \[ x - 8 = 0 \quad \Rightarrow \quad x = 8 \] \[ x + 5 = 0 \quad \Rightarrow \quad x = -5 \] Thus, the values of \( x \) that are NOT in the domain of \( h \) are: \[ x = 8, -5 \] So, the final answer is: \( x=8, -5 \)
