How to write a function that expresses f (x)

Question

Mathematics

John Callahan

14 March, 11:21

How to write a function that expresses f (x)

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Answers (1)

Know the Answer?

Yosef Haley · Answer 1

Lets write

(x) = (1 / 2) f (x) + (1 / 2) f (x) + (1 / 2) f (-x) - (1 / 2) f (-x)

which gives us

= (1 / 2) (f (x) + f (-x)) + (1 / 2) (f (x) - f (-x))

let

g (x) = (1 / 2) (f (x) + f (-x))

check that g (x) is even

g (-x) = (1 / 2) (f (-x) + f (x)) = g (x)

let

h (x) = (1 / 2) (f (x) - f (-x))

check that h (x) is odd

h (-x) = (1 / 2) (f (-x) - f (x)) = - (1 / 2) (f (x) - f (-x)) = - h (x)