use the pair of functions f and g to find the following valu

use the pair of functions f and g to find the following values if they exist.

Solution

The question from composite functions

we generally need to find (f o g)(x) , ( g o f)(x) , (f o f)(x) and (g o g)(x)

i) (f o g) (x)

Plug x= 2x-1 in f(x)

f(x) = sqrt(x+3) = sqrt( 2x-1 +3) = sqrt( 2x+2)

ii) ( g o f )(x)

Plug x= sqrt(x +3) in g(x)

( g o f )(x) = 2(sqrt(x+3)) -1

iii) (g o g)(x)

plug x= 2x-1 in g(x)

(g o g)(x) = 2(2x-1) -1 = 4x -3

iv) (f o f)(x)

x = sqrt(x +3)

( f o f)(x) = sqrt(sqrtx +3) +3)

Now we can find values of these composite functions at various values of x= 0, 1, -1....so on by plugging x in the se functions