Question

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).

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).