Given the functions fx 5x 1 and gx square root x find the

Given the functions f(x) = -5x - 1 and g(x) = square root x, find the following functions and their domains: Write the domains using interval notation. If the quantities do not exist, write \"undefined\" in the blank provided. You have 3 attempt(s) remaining before you will receive a new version of this problem.

Solution

f(x) = -5x -1 , g(x) = x

(f o g)x = f(g(x))

==> (f o g)x = f(x)

==> (f o g)x = -5x -1

Hence (f o g)x = -5x -1

(g o f)x = g(f(x))

==> (g o f)x = g(-5x -1)

==> (g o f)x = (-5x -1)

Hence (g o f)x = (-5x -1)

Domain of (f o g)x ==> value under square root is greater than zero

==> x >= 0

Hence domain is [0 , )

Domain of (g o f)x ==> value under square root is greater than zero

==> (-5x -1) >= 0

==> 5x + 1 <= 0

==> 5x <= -1

==> x <= -1/5

Hence domain of (g o f)x = (- , -1/5]