2008 AMC 12A Problem 12

Problem 12 of 25IntermediateAlgebra

A function

f

has domain

[0, 2]

and range

[0, 1].

(The notation

[a, b]

denotes

\{x : a \le x \le b\}.

) What are the domain and range, respectively, of the function

g

defined by

g(x) = 1 - f(x + 1)?

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Solution

The value

f(x + 1)

is defined when

0 \le x + 1 \le 2,

that is,

-1 \le x \le 1,

so the domain of

g

is

[-1, 1].

As

f(x + 1)

ranges over

[0, 1],

the value

1 - f(x + 1)

ranges over

[0, 1]

as well, so the range of

g

is

[0, 1].

Thus, B is the correct answer.

More practice

Concepts: function

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.