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QuizMultiple Choice

Composition of Functions — Quiz

Question 1 • Mathematics III

If m times x is equal to the fraction with numerator x plus 5 and denominator x minus 1 and n times x is equal to x minus 3 , which function has the same domain as open paren m circ n close paren times x ?

Answer
A
h of x is equal to the fraction with numerator 11 and denominator x minus 4
B
h of x is equal to the fraction with numerator x plus 5 and denominator 11
C
h of x is equal to the fraction with numerator 11 and denominator x minus 3
D
h of x is equal to the fraction with numerator 11 and denominator x minus 1

Explanation

For (m ∘ n)(x), substitute n(x) = x − 3 into m(x) = (x + 5)/(x − 1). This gives (x + 2)/(x − 4), which is undefined when x = 4, so its domain is all real numbers except 4. Choice A, h(x) = 11/(x − 4), has the same domain.

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