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1.Relation and Function
normal
જો વિધેય $f(x)$ માટે $f\left( {x + \frac{1}{x}} \right) = {x^2} + \frac{1}{{{x^2}}};$ હોય તો $(fof )$ $\sqrt {11} )$ =
A
$9$
B
$81$
C
$79$
D
$\sqrt {11}$
Solution
$f\left(x+\frac{1}{x}\right)=x^{2}+\frac{1}{x^{2}}=\left(x+\frac{1}{x}\right)^{2}-2$
Now replace $x+\frac{1}{x}$ by
$\Rightarrow f(x)=x^{2}-2$
$\Rightarrow f o f(x)=\left(x^{2}-2\right)^{2}-2$
$\therefore$ fof $(\sqrt{11})=9^{2}-2=79$
$f o f(\sqrt{11})=79$
Standard 12
Mathematics
