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Composition of Exponential and Logarithmic Functions

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The functions ff and gg are defined by f(x)=ex1f(x) = e^{x-1} and g(x)=ln(x)+1g(x) = \ln(x) + 1. For x>0x > 0, which of the following is an expression for h(x)=(fg)(x)h(x) = (f \circ g)(x)?

A

xx

B

x1x - 1

C

ln(x)+1\ln(x) + 1

D

eln(x)+1e^{\ln(x) + 1}

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