WBJEE · Maths · Functions
Consider the functions \(f_{1}(x)=x, f_{2}(x)=2+\log _{e} x, x>0\). The graphs of the functions intersect.
- A once in \((0,1)\) but never in \((1, \infty)\)
- B once in \((0,1)\) and once in \(\left(e^{2}, \infty\right)\)
- C once in \((0,1)\) and once in \(\left(e, e^{2}\right)\)
- D more than twice in \((0, \infty)\)
Answer & Solution
Correct Answer
(C) once in \((0,1)\) and once in \(\left(e, e^{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\mathrm{f}_{1}(\mathrm{x})=\mathrm{x}, \mathrm{f}_{2}(\mathrm{x})=2+\log _{\mathrm{e}} \mathrm{x}\) Let \(g(x)=f_{2}(x)-f_{1}(x)=2+\log _{e} x-x\) \(g\left(o^{+}\right) 0, g(e)>0, g\left(e^{2}\right) < 0\) and value of \(g(x)\) for all \(x \geq e^{2}\) is negative.…
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