Use f(x) = ?2x, g(x) = square root of x and h(x) = |x| to find...

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)

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Expert Solution

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.

milcah answered 1 year ago

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