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Need help with the composition of functions. I have attached a screenshot of the question.

Need help with the composition of functions. I have attached a screenshot of the question-example-1

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3 votes

using (f ○ g)(x) = f(g(x))

substitute x =
(7)/(x) into f(x)

f(
(7)/(x)) = 4 / (
(7)/(x) - 3 ) ×
(x)/(x)

=
(4x)/(7-3x)

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 7 - 3x = 0 ⇒ x =
(7)/(3)

domain : x ∈ ( - ∞,
(7)/(3)) ∪ (
(7)/(3), + ∞ )


User Broots Waymb
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