TS EAMCET · Maths · Functions
A function \(f: \mathbf{R} \rightarrow \mathbf{R}\) is such that \(f(\mathrm{l})=2\) and \(f(x+y)=f(x) \cdot f(y) \forall x, y\). The area (in square units) enclosed by the lines \(2|x|+5|y| \leq 4\) expressed interms of \(f(1), f(2)\) and \(f(4)\) is
- A \(\frac{f(4)}{f(1)+2 f(2)}\)
- B \(\frac{f(4)}{1+f(2)}\)
- C \(\frac{2 f(4)}{2 f(1)+f(2)}\)
- D \(\frac{f(4)}{2 f(1)+f(2)}\)
Answer & Solution
Correct Answer
(B) \(\frac{f(4)}{1+f(2)}\)
Step-by-step Solution
Detailed explanation
Given, \(f(x+y)=f(x) \cdot f(y)\) \(\therefore \quad f(x)=a^x\) \(f({1})=a^{{l}}=2 \Rightarrow a=2\) \(\therefore \quad f(x)=2^x\) Area enclosed by the lines \(2|x|+5|y| \leq 4\) \(4\left(\frac{1}{2} \times 2 \times \frac{4}{5}\right)=\frac{16}{5}\)…
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