Question

F:x→(x+1/x+3), x≠3 and g:x→（6/x-2), x≠2, find f²(4) and g²(1/2)​

Answer 1

`f^2(4) = ((25)/(49))\\g^2((1)/(2) ) = 16`

Explanation:

Here, given:

`f(x) = ((x+1)/(x+3) ), g(x) = ((6)/(x-2) )`

Now, here to find the values of
`f^2(4), g^2((1)/(2))`

As we know:
`f^n(x) = (f(x))^n`

Now, substituting x = 4 in f(x):

`f(4) = (4 +1)/(4+3) = (5)/(7) \\\implies f^4 = (f(4))^2 = ((5)/(7) )^2 = (25)/(49) \\\implirs f^((4)) = ( (25)/(49))`

Now, substituting x = 1/2 in g(x):

`g((1)/(2) ) = (6)/((1)/(2)-2) = (6)/(-(3)/(2)) \\\\ g((1)/(2) ) = -6* ((2)/(3) ) = -4\\\implies g^2{((1)/(2)) = ( g((1)/(2) ))^2 = (-4 )^2 =16 \\\\\implies g^2{((1)/(2)) = 16`