Question

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

Answer 1

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 ∈ (- ∞, $\frac{1}{3}$) ∪ ($\frac{1}{3}$, + ∞ )