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Functions f,g:R→R are defined, respectively, by f(x)=x2+3x+1 ,           g(x)=2x−3 , find

(i) f∘g

(ii) g∘f

(iii) f∘f

(iv) g∘g

0 3 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    This is a Long Answer Type Question as classified in NCERT Exemplar

    Sol:

      (i)       fog  ⇒  f[(g(x)]  =  [g](x)2+3[(g(x)]+1                                                     =(2x−3)2+3(2x−3)+1                                                     =4x2+9−12x+6x−9+1=4x2−6x+1  (ii)         gof  ⇒  g[f(x)]=2[x2+3x+1]−3                                                      =2x2+6x+2−3=2x2+6x+1  (iii)        fof  ⇒  f[(f(x)]=[f(x)]2+3[f(x)]+1                                                        =(x2+3x+1)2+3(x2+3x+1)+1                                                        =x4+9x2+1+6x3+6x+2x2+3x2+9x+3+1                                                        =x4+6x3+14x2+15x+5  (iv)  gog  ⇒g[g(x)]=2[g(x)]−3=2(2x−3)−3=4x−6−3=4x−9

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