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18. If \( 2^{f(x)}=\frac{2+x}{2-x}, x \in(-2,2) \) and \( f(x)=\lambda f\left(\frac{8 x}{4+x^{2}}\right) \) then value of ' \( \lambda \) ' will be(1) 2(2) \( \frac{1}{2} \)(3) 1(4) -1 |
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Answer» 2f(x) = \(\frac{2+x}{2-x}\) ......(1) f(x) = \(\lambda f(\frac{8x}{4+x^2})\) f(1) = \(\lambda f(\frac{8}{5})\) ......(2) 2f(1) = \(\frac31=3\) From (i) ⇒ f(1) = log23 2f(\(\frac85\)) = \(\frac{2+\frac85}{2-\frac85}\) = \(\frac{18}2 =9\) \(\therefore\) f(\(\frac85\)) = log29 = log232 = 2log23 \(\therefore\) 2\(\lambda\) log23 = log23 From (2) f\(\lambda\) = \(\frac12\) |
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