How to write a function that expresses f (x)

Question

Mathematics

Angelique Randolph

23 April, 06:13

How to write a function that expresses f (x)

+2

Answers (1)

Know the Answer?

Callum Haas · 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)