CUET Preparation Today
If $f(x)+2f(1-x)=x^2+2,∀\,x∈R$, then f(x) is given as |
$\frac{(x-2)^2}{3}$ $x^2-2$ 1 none of these |
$\frac{(x-2)^2}{3}$ |
$f(x)+2f(1-x)=x^2+2$ …(i) Replacing x by 1 – x in (i), we get ⇒ $f(1-x)+2f(x)=(1-x)^2+2$ $⇒ f(1-x)+2f(x)=x^2-2x+3$ …(ii) Eliminating f(1− x) from (i) and (ii), $f(x)=\frac{(x-2)^2}{3}$ |
