$f[{x^2} + yf(z)] = xf(x) + zf(y)$<p></p>$\forall {\rm{ }}x,y,z \in \mathbb{R}$<p></p>$f=?$

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$f[{x^2} + yf(z)] = xf(x) + zf(y)$
$\forall {\rm{ }}x,y,z \in \mathbb{R}$
$f=?$

Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096 $ $\therefore 2^n = 4096 =2^{12} $ $\Rightarrow n = 12 $ Greatest coefficient = ${}^{12}{C_6} = 924$

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$f[{x^2} + yf(z)] = xf(x) + zf(y)$
$\forall {\rm{ }}x,y,z \in \mathbb{R}$
$f=?$

Popular posts from this blog

Sum of the coefficients in the expansion of $(x+y)^n$ ....

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Updates ...

$f[{x^2} + yf(z)] = xf(x) + zf(y)$$\forall {\rm{ }}x,y,z \in \mathbb{R}$$f=?$

Popular posts from this blog

Sum of the coefficients in the expansion of $(x+y)^n$ ....

$f[{x^2} + yf(z)] = xf(x) + zf(y)$
$\forall {\rm{ }}x,y,z \in \mathbb{R}$
$f=?$