A calculus problem by crazy singh

Calculus Level 2

Find f ( 1 2 ) f\left( \frac { 1 }{ 2 } \right) if f ( g ( x ) ) = x 4 + x 2 1 + x 2 f\left( g\left( x \right) \right) =\frac { { x }^{ 4 }+{ x }^{ 2 } }{ 1+{ x }^{ 2 } } and g ( x ) = 1 − x 2 g\left( x \right) =1-{ x }^{ 2 }


The answer is 0.5.

Crazy Singh by crazy singh , 31, India

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1 solution

Pranav Deshpande
Mar 27, 2014

Let g(x)=y=1-x^2 so, -y = -1 + x^2 i.e. -y+1 = x^2 which is nothing but f(g(x)) in the form of f(y), thus put y=0.5 to get the answer

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