WBJEE · Maths · Functions
Consider the function \(f(x)=(x-2) \log _e \cdot x\). Then the equation \(x \log _e x=2-x\)
- A has at least one root in (1, 2)
- B has no root in (1, 2)
- C is not at all solvable
- D has infinitely many roots in (–2, 1)
Answer & Solution
Correct Answer
(A) has at least one root in (1, 2)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Hint : Let } g(x)=x \log _e x-2+x \\ & g^{\prime}(x)=1+\log _e x+1=2+\log _e x \\ & g(1) \cdot g(2)=-1 \times\left(2 \log _e 2\right)=-v e\end{aligned}\)
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