For any given function f (x), define g (x) = - f (x) h (x) = f ( - x) Explain how g (x) is different from h (x) using an example. Explain if or when it would be possible for g (x) = h (x).

Question

Bradley Novak

Mathematics

13 November, 03:18

For any given function f (x), define g (x) = - f (x) h (x) = f ( - x) Explain how g (x) is different from h (x) using an example. Explain if or when it would be possible for g (x) = h (x).

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Joy · Answer 1

Case (i) : Let f (x) = cos x

-f (x) = - cos x

So, g (x) = - cos x.

f (-x) = cos (-x)

So, h (x) = cos x.

Hence, g (x) is different from h (x).

Case (ii) : Let f (x) = sin x

-f (x) = - sin x

So, g (x) = - sin x

f (-x) = sin (-x)

= - sin x

So, h (x) = - sin x.

Hence, g (x) = h (x).