Question

let f(x)=2x square and g(x)=x square/3 find fof and gog

Answer 1

Answer:

the answer is

Step-by-step explanation:

f(x)=x2+3x+1,g(x)=2x−3

(i) fog=f(g(x))=f(2x−3)=(2x−3)2+3(2x−3)+1

=4x2+9−12x+6x−9+1

∴fog=4x2−6x+1

(ii) gof=g(f(x))=g(x2+3x+1)=2(x2+3x+1)−3

=2x2+6x+2−3

∴gof=2x2+6x−1

(iii) fof=f(f(x))=f(x2+3x+1)=(x2+3x+1)2+3(x2+3x+1)+1

=x4+9x2+1+6x2+6x+2x2+3x2+9x+3+1

∴fof=x4+6x3+14x2+15x+5

(iv) gog=g(g(x))=g(2x−3)=2(2x−3)−3

=4x−6−3

∴gog=4x−9.