Question
\[ g(x)=\frac{x-7}{x^{2}+10 x+16} \] Find \( g(-5) \) Simplify your answer as much as possible. If applicable, click on "Undefined". \[ g(-5)= \] \( \square \) Undefined
Ask by Morrison Ingram. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( g(-5) = \frac{4}{3} \)
Solution
Substitute \( x=-5 \) into the expression \( \frac{x-7}{x^{2}+10x+16} \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(\frac{x-7}{x^{2}+10x+16}\)
- step1: Substitute:
\(\frac{-5-7}{\left(-5\right)^{2}+10\left(-5\right)+16}\)
- step2: Multiply the numbers:
\(\frac{-5-7}{\left(-5\right)^{2}-50+16}\)
- step3: Subtract the numbers:
\(\frac{-12}{\left(-5\right)^{2}-50+16}\)
- step4: Calculate:
\(\frac{-12}{-9}\)
- step5: Reduce the fraction:
\(\frac{4}{3}\)
The value of \( g(-5) \) is \( \frac{4}{3} \) or \( 1\frac{1}{3} \) or \( 1.\dot{3} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg


Extra Insights
To find \( g(-5) \), substitute \( x = -5 \) into the function: \[ g(-5) = \frac{-5 - 7}{(-5)^2 + 10(-5) + 16} = \frac{-12}{25 - 50 + 16} = \frac{-12}{-9} = \frac{4}{3} \] Thus, \( g(-5) = \frac{4}{3} \).