Question

If f (x) = e^x and g(x) = log_e x, then which of the following is true ?

(a) f {g (x)} ≠ g{f (x)} 

(b) f {g (x)} = g{f (x)} 

(c) f {g (x)} + g{f (x)} = 0

(d) f {g (x)} – g{f (x)} = 1

Answer 1

Answer :  (b) f {g (x)} = g{f (x)}

f (x) = e^x and g(x) = log_e x 

∴ f {g (x)} = f (log_e x) = e^{log_e x} = x 

= g{f (x)} = g (e^x ) = log_e^ex = x 

∴ f {g(x)} = g{f (x)}.