Answers Algebra II PretestQuestion 10

10

lesson pretestMultiple Choice

Pretest

Question 10 • Algebra II

For which pair of functions is open paren f circ g close paren times x is equal to x ?

Answer

A

f of x is equal to 2 over x and g of x is equal to 2 over x

B

f of x is equal to the fraction with numerator x minus 2 and denominator 3 and g of x is equal to 2 minus 3 x

C

f of x is equal to 1 half x minus 2 and g of x is equal to 1 half x plus 2

D

f of x is equal to x squared and g of x is equal to 1 over x

Explanation

For choice A, substitute g(x) = 2/x into f(x) = 2/x: f(g(x)) = 2/(2/x) = x, for x ≠ 0. Thus the composition equals x wherever both functions are defined. The other choices do not simplify to x.

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