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Show that the function f defined by $f(x) = (x - 1) e^x + 1$ is an increasing function for all x > 0.

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$f(x) = (x - 1) e^x + 1$

$f^{\prime}(x)=x e^{x}$

$f^{\prime}(x)=x e^{x} >0 $ for all $x>0$

$f $ is an increasing function for $ x>0$

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