Composite Function!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

Find f(1/2) if [f o g](x)= x^4+x^2/1+x^2 and g(x)=1-x^2

Answer 1

Given that [f o g] (x)= (x⁴+x²)/(1+x²)

Takeout common factor x²

f(g(x)=  x² (x²+1)/(1+x²)

f(g(x)=x²

Given g(x)=1 - x²

Substitute g(x)=1 - x² in f(g(x)=x²

f(x)=(1 - x²)²

To find f(1/2) substitute 1/2 in f(x)

f(1/2)=[1 - (1/2)²]²
 =[1 - (1/4)]²
=(3/4)² = 9/16

there fore f(1/2)= 9/16