Question

Need help finding the quotient of two functions

Answer 1

($\frac{g}{f}$)(x) = $\frac{8}{x+4}$ ÷ $\frac{7}{x}$

= $\frac{8}{x+4}$ × $\frac{x}{7}$ = $\frac{8x}{7x+28}$

The denominator cannot be zero as this would make the rational function undefined. Equating the denominator to zero and solving gives the value that x cannot be

solve 7x + 28 = 0 ⇒ x = - 4 ← excluded value

domain is x ∈ (- ∞, - 4 ) ∪ (- 4, + ∞ )