Given fx - 2x - 1-x - 1- Find - fa

The correct option is B 2a 1/a + 1 . #160; f(x)=2x 1x+1 f(a)=2a 1a+1 ...

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Definition of Functions

Given fx = ...

Question

Given $f (x) = \frac{2 x - 1}{x + 1}$ . Find : f(a)

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\frac{2 a - 1}{a + 1}

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\frac{2 a + 1}{a - 1}

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Solution

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\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}

Solve for $x : \frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}$

f (x) =

∣ ∣ ∣ ∣ ∣ \begin{matrix} (1 + 3 x)^{2 a} & (1 + 2 x)^{3 b} & 1 1 & (1 + 3 x)^{2 a} & (1 + 2 x)^{3 b} (1 + 2 x)^{3 b} & 1 & (1 + 3 x)^{2 a} \end{matrix} ∣ ∣ ∣ ∣ ∣

x = \frac{\sqrt{2 a + 1} + \sqrt{2 a - 1}}{\sqrt{2 a + 1} - \sqrt{2 a - 1}}

x^{2} - 4 a x + 1 = 0

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(i) $a + 2$

(ii) $2 a - 1$

(iii) $2 a + 3 b$

(iv) $3 b - 2 a$

(v) $2 x + \frac{1}{x}$

(vi) $x - \frac{1}{2}$

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