Question

if f (x)=3+X, g (x)=x-4, then check whether f○g=g○f​

Answer 1

Step-by-step explanation:

Given :f(x) =3+x,g(x)=x-4

To find :f°g=g°f

Solution :hint x-4=0;x=4+0=4

f(x)=0

f(x)=3+(4)=7

Answer 2

When f (x)=3+X, g (x)=x-4, then fоg $\neq$ gоf​  

Given:

f (x)=3+X   and  g (x)=x-4

To find:

Check whether fоg = gоf​

Solution:

NOTE:

If f(x) and g(x) are two functions, then the function gof is defined by

(gof)(x) = g[f(x)], and it is called as composition of f and g.

Given f (x)=3+x   and  g (x)=x-4

From the above data, fоg = f [g(x)]

take x = g(x) = (x-4)

fоg = f [g(x)] = 3 +(x - 4) = x - 1

⇒ fоg = x - 1 -----(1)

From the above data, gоf = g [f(x)]

take x = f(x) = 3+x

gоf = g [f(x)] = x - (3 + x) = x - 3 - x = -3

⇒ gоf = - 3 -----(2)

From (1) and (2)

fоg $\neq$ gоf​  

Therefore,

if f (x)=3+X, g (x)=x-4, then fоg $\neq$ gоf​  

#SPJ2