Question

If f(x)= x, g(x)= 2x and h(X)= X+4. Show That (f•g)•h=f(g•h)​

Answer 1

Answer:

GIVEN:

f(x) = x

g(x) = 2x

h(x) = x+4

To show: (fog)oh = fo(goh)

LHS : (fog)oh

   (fog)oh = (fog)(h(x)

                = f{g {h(x)} }

                = f {g {x+4} }   (sub the value of h(x))

                 = f {2{x+4}}     [sub x + 4 in g(x) = 2x ]

                 = f {2x + 8}

                  = 2x + 8

RHS : fo(goh)

   fo(goh) = f {g {h(x)} }

                 = f {g {x+4} }   (sub the value of h(x))

                 = f {2{x+4}}     [sub x + 4 in g(x) = 2x ]

                 = f {2x + 8 }      

                 =  2x +8  

comparing LHS and RHS,

(fog)oh = fo(goh)

hece, showed.