f(x)= square root of x and g(x)=^3square root 1 - x. Show the domain and fully simplify the expression. a) f x g b) g x f c) f x fFor g(x) the...

f(x) = sqrtx = x^(1/2)

g(x) =
3^sqrt(1-x).

To determine the domain and the functions: f
(g(x), and g(f(x) and
f((x).

Solution:

domain:

The
domain sqrt of x = x^(1/2) is x > = 0. The domain of sqrt(x-1) is x-1 >=
0. Or x > = 1. Both together the domain is x >
1.

f*g =f(g(x)

f*g = sqrt {
g(x)}

f*g = sqrt {
3^sqrt(x-1)

f*g = 3^ ((1/2)sqrt(x-1)), by index law sqrta =
a^(1/2).

f*g = 3
^[0.5sqrt(x-1)]

g*f =
g(f(x))

g*f =3^sqrt (f(x))

g*f
= 3^(sqrt(sqrtx))

g*f =
3^(sqrt(x^(1/2)))

g*f= 3 ^(x
^((1/2)*(1/2)))

g*f =
3^(x^0.25)

f*f =
f((f(x))

f*f = sqrt {
sqrtx}

f*f= sqrt(x^(1/2)

f*f=
x^((1/2)(1/2)) = x^0.25.