5
QuizMultiple Choice

Function Inverses — Quiz

Question 5 • Mathematics III

If f of x is equal to 3 x and g of x is equal to 1 third x , which expression could be used to verify that g of x is the inverse of f of x ?

Answer
A
1 third times 3 x
B
3 x open paren x over 3 close paren
C
1 third times open paren 1 third x close paren
D
open paren 1 third x close paren times 3 x

Explanation

To verify that g is the inverse of f, substitute f(x) = 3x into g(x) = x/3. This gives g(f(x)) = (1/3)(3x) = x, so choice D, “1 third times 3x,” verifies the inverse relationship.

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