In: Math
Use f(x) = ?2x, g(x) = square root of x and h(x) = |x| to find and simplify expressions for the following functions and state the domain of each using interval notation. a . (h ? g ? f)(x) b. (h ? f ? g)(x) (g ? f ? h)(x)
a) h o go f(x)
we can write this as, h o g(f(x)) = h o g(-2x)
h (g(-2x)) = h ( )
h ( ) =
in order to get the square root term positive, x must be negative. So, domain of the function
b. (h ? f ? g)(x)
h o f (g(x)) = h o f ()
= h ( f() = h()
= =
=
All non-negative numbers can be of domain. So,
c. (g ? f ? h)(x)
g(f(h(x))) = g(f()
= g()
=
In this case, the function is not having a domain as only x = 0.