Question

f(x)=x^2 , g(x)=3 find fof , gof, fof, gog​

Answer 1

Answer:

Given that,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 - 12x + 9 + 6x - 9 + 1

= 4x2 - 6x + 1

(ii) gof = g(f(x)

= g(x2+3x+1)

= 2(x2+3x+1)-3

= 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

= x4 + 6x3 + 14x2 + 15x + 5

(iv) gog = g(g(x))

= g(2x-3)

= 2(2x-3)-3

= 4x - 6 - 3

= 4x - 9