Question

check whether FOG=GOF. f(x)=4x2-1,g(x)=1+x​

Answer 1

fog = f(g(x))

= f(1+x)

=[ 4(1+x)^2]- 1= 4(1+2x+x^2)-1

= 4+8x+4x^2 -1

= 4x^2 +8x +3

gof= g(f(x))

= g(4x^2 -1)

= 1+ 4x^2 -1 = 4x^2

therefore fog is not equal to gof