Question

IF F(X)=2x+3 g(x)=1.2x h(x)=3x prove that fo(goh)=(fog)oh
​

Answer 1

Step-by-step explanation:

f(x) = 2x+3

g(x) = 1.2x

h(x) = 3x

To prove f o (g o h) = (f o g) o h,

take LHS = f o (g o h)

                = f o (g(h(x)))

                = f o g(3x)

                = f (g(3x))

                = f(1.2(3x))

                = f(3.6x)

                = 2(3.6x)+3

                = 7.2x+3 ------------------ (1)

_________________________________

take f o g

                 => f(g(x))

                 = f(1.2x))

                 = 2(1.2x)+3

                 = 2.4x +3

_________________________________

now RHS = (f o g) o h

                = (f o g) (h(x))

                = (f o g) (3x)

                = 2.4(3x) +3

                = 7.2x + 3 ---------------- (2)  

from (1) & (2)

we have LHS = RHS

=> f o (g o h) = (f o g) o h

hence proved