If $f(x)=e^x ; g(x)=\ln (x)$ for all $x \in[1, \infty)$, then $f \circ g$ is ____

Question

If $f(x)=e^x ; g(x)=\ln (x)$ for all $x \in[1, \infty)$, then $f \circ g$ is ____, A one-one function, An onto function, Not a function, Bijective

MARKS App · Accepted Answer

For $x \in[1, \infty), f(x)=e^x$ and $g(x)=\ln x$ $\therefore(f \circ g)(x)=e^{\ln x}=x, x \in[1, \infty)$ is a bijective function. Hence, option (d) is correct.

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