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hichkok12 [17]
4 years ago
5

Need Help finding the composition of two rational functions. I attached a screenshot of the question i could use some help with

Mathematics
1 answer:
yaroslaw [1]4 years ago
8 0

using (f ○ g )(x) = f(g(x))

f(g(x) =f( \frac{1}{x})

substitue x = \frac{1}{x} in f(x)

= \frac{1}{x} / \frac{1}{x} - 3 × \frac{x}{x}

= \frac{1}{1-3x}

the denominator of f(g(x)) cannot be zero as this would make f(g(x)) undefined. Equating the denominator to zero and solving gives the value that x cannot be

solve 1 - 3x = 0 ⇒ - 3x = - 1 ⇒ x = \frac{1}{3} ← excluded value

domain is x ∈ (- ∞, \frac{1}{3}) ∪ (\frac{1}{3}, + ∞ )



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