f ( x ) = f ( − x ) f(x)=f(-x)

Algebra Level 1

For set A = { − 9 , − 2 , 0 , 2 , 9 } , A=\{-9, -2, 0, 2, 9\}, how many functions f : A → A f: A \to A exist such that f ( x ) = f ( − x ) ? f(x)=f(-x)?

125 250 500 625

Ajay Dutta by Ajay Dutta , 24, India

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1 solution

each function has three choices for the images. One for 9,-9, one for 2,-2 and one for 0. It can chose any of the five elements in the set for each of these choices.

So, 5^3 = 125

0 Helpful 0 Interesting 0 Brilliant 0 Confused

The function looks like this:

f(-9) = x

f(9) = x

f(2) = y

f(-2) = y

f(0) = z

You have 5 choices for each of x,y and z. So, you can chose x,y and z in 5 5 5 ways, right?

Agnishom Chattopadhyay - 7 years, 3 months ago

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