Question

Suppose that the functions $h$ and $f$ are defined as follows. $h(x) = \frac{4}{9x}$, $x \neq 0$ $f(x) = 4x - 3$ Find the compositions $h \circ h$ and $f \circ f$. Simplify your answers as much as possible. (Assume that your expressions are defined for all $x$ in the domain of the composition. You do not have to indicate the domain.) $(h \circ h)(x) = (f \circ f)(x) = $

          Suppose that the functions $h$ and $f$ are defined as follows.
$h(x) = \frac{4}{9x}$, $x \neq 0$
$f(x) = 4x - 3$
Find the compositions $h \circ h$ and $f \circ f$.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all $x$ in the domain of the composition. You do not have to indicate the domain.)
$(h \circ h)(x) = 
(f \circ f)(x) = $

Suppose that the functions h and f are defined as follows.
h(x) = (4)/(9x), x ≠ 0
f(x) = 4x - 3
Find the compositions h ∘ h and f ∘ f.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)
(h ∘ h)(x) =
(f ∘ f)(x) =

Added by John F.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Dayna Kitsuwa

Step 1

So, we have: h(g(x)) = (g(x))^4 - 4(g(x)) - 3 Now, let's substitute g(x) = √(x + 6) into h(g(x)): h(g(x)) = (√(x + 6))^4 - 4(√(x + 6)) - 3 To simplify this expression, we can expand (√(x + 6))^4 using the binomial theorem: (√(x + 6))^4 = (x + 6)^(4/2) = (x + Show more…

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Suppose that the functions h(x) and g(x) are defined as follows: h(x) = x^4 - 4x - 3 g(x) = âˆš(x + 6) Find the compositions h(g(x)) and g(h(x)). Simplify your answer as much as possible. Indicate the domain.