If f (x) = ex and g(x) = loge x, then which of the following is true ?

1.	If f (x) = ex and g(x) = loge 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» 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)}.

If f (x) = ex and g(x) = loge 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»

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)}.