Question

Write the inverse of g(x) = e x g -1(x) = _____.

Answer 1

Answer:

$g^{-1} (x) = \ln x$

Step-by-step explanation:

From the definition if inverse function we can say if y = f(x) and x = h(y) then h(x) is the inverse function of f(x).

Here the given function is $g(x) = e^{x}$ and we have to find the $g^{-1} (x)$ i.e. the inverse function of g(x).

Now, let us assume $y = g(x) = e^{x}$

Now, taking ln both sides we get, $\ln y = \ln e^{x} = x \ln e = x$  

{Since $\ln e = 1$}

⇒ $x = \ln y$

Therefore, $g^{-1} (x) = \ln x$ (Answer)