Composition Of Functions And Invertible Function

To find

(gof)(x)

, which means

g(f(x))

, we follow these steps:

1. We start with the function

f(x)%3De%5Ex

2. Determine

f(x)

: Since

f(x)%20%3D%20e%5Ex

, we substitute into the function

g(x)%20%3D%20%5Cln%20x

to get

g(f(x))%20%3D%20g(e%5Ex)

3. Now, substitute

e%5Ex

into

g(x)

g(e%5Ex)%20%3D%20%5Cln(e%5Ex)

4. Simplify

%5Cln(e%5Ex)

: Using the logarithmic identity

%5Cln(e%5Ex)%20%3D%20x

, we find

(gof)(x)%20%3D%20x

Therefore, the result of the composition

(gof)(x)

x

Hence, the correct answer is

x

Chapter Questions
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