Q7 of 215 Page 3

Let f be any real function and let g be a function given by g(x) = 2x. Prove that gof = f + f.

We are given that f is a real function and g is a function given by

g(x) = 2x

To prove; gof=f + f.

L.H.S

gof(x) = g(f(x)) = 2f(x)

=f + f = R.H.S

gof=f + f

Hence proved

If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?

Let f, g, h be real functions given by f(x) = sin x, g(x) = 2x and h(x) = cos x. Prove that fog = go(fh).

If and g(x) = log_ex are two real functions, then describe functions fog and gof.