Question

given f(x) = 5x+2, g(x) =2x-3, h(x) =3x+1 , verify fo(goh) =(fog) oh​

Answer 1

EXPLANATION.

GIVEN.

=> f(x) = 5x + 2

=> g(x) = 2x - 3

=> h(x) = 3x + 1

verify that = fo(goh) = (fog)oh.

=> L.H.S. = fo(goh).

=> goh = g ( h(x))

=> g ( 3x + 1 )

=> 2 ( 3x + 1 ) - 3

=> 6x + 2 - 3

=> 6x - 1 = goh

=> fo(goh) = f(goh(x)).

=> f ( 6x - 1 )

=> 5 ( 6x - 1 ) + 2

=> 30x - 5 + 2

=> 30x - 3 = fo(goh).

R.H.S = (fog)oh.

=> fog = f (g(x))

=> f ( 2x - 3 )

=> 5 ( 2x - 3 ) + 2

=> 10x - 15 + 2

=> 10x - 13 = fog

=> (fog)oh = fog(h(x))

=> fog ( 3x + 1 )

=> 10 ( 3x + 1 ) - 13

=> 30x + 10 - 13

=> 30x - 3 = (fog)oh.

Therefore,

=> fo(goh) = (fog)oh.

HENCE VERIFIED.