Sets, Relations & Functions
Range of Rational Function
nta_pyq_2024_apr
Grade 11
Question:
Let the sum of the maximum and the minimum values of the function $f(x)=\dfrac{2x^2-3x+8}{2x^2+3x+8}$ be $\dfrac{m}{n}$, where $\gcd(m,n)=1$. Then $m+n$ is equal to:
Step-by-Step Solution
Key Concept: Set $y=f(x)$: rearrange to $x^2(2y-2)+x(3y+3)+(8y-8)=0$. Use discriminant $\geq0$ to find range of $y$.
Max $=11/5$, min $=5/11$. Sum $=146/55$. $m+n=201$.
Correct Answer: 2