IonaSkye3 IonaSkye3

07-06-2014
Mathematics

Answered

The functions f and g are defined on a suitable domain by F(x)=x^2-1 and g(x)=x^2+2'
A) find the expression for f(g(x))
B) factorise f(g(x))

Answer :

konrad509 konrad509

07-06-2014

[tex]f(x)=x^2-1\\ g(x)=x^2+2\\ f(g(x))=(x^2+2)^2-1=x^4+4x^2+4-1=x^4+4x^2+3\\\\ x^4+4x^2+3=\\ x^4+x^2+3x^2+3=\\ x^2(x^2+1)+3(x^2+1)=\\ (x^2+3)(x^2+1)[/tex]

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