If \(f(x) = e^x\) and \(g(x) = \log_e x = \ln x\), then \((gof)(x)\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → x
In the composition gof, f acts first and g acts on its output:
\((gof)(x) = g(f(x))\)
\(= g(e^x)\)
\(= \log_e(e^x)\)
\(= x\)
The logarithm to base e and the exponential function are inverses of each other, so one undoes the other.