If f(x) = 1-ln(x) and g(x) = e^x-1, I'm being asked to find the simplified form of (g o f)(x), but I'm not even sure how to start. The answer is apparently 1/x. Can someone please help me? Thanks.

Question

lgbasallote · Answer

do you know that g o f means g(f(x))?

anonymous · Answer

Yeah, which means it's $$e^{1-\ln(x)-1}$$ but I'm not sure how to simplify that. :(

apoorvk · Answer

When you are asked "g o f(x)", you need to find g(f(x)), just as lgbasallote says up here^.

So, instead of 'x', substitute every 'x' in g(x) with f(x). Thus,

$$g(f(x)) =  e^{f(x)} - 1$$
$$or,  g(f(x)) =  e^{1 - lnx} - 1$$

Now simplify this equation and arrive at your answer. But basically, this^ is what you need to do in such questions.

apoorvk · Answer

Oh am sorry - okay simplifying - are you familiar with log rules?

anonymous · Answer

Ohh log rules. Of course. Why didn't I think of that? Thanks a lot!