f is a continous function in $\left[a,b\right]$; g is a continuous function in [b,c]. A function h(x) is defined as $h\left(x\right)=f\left(x\right)f\text{or}x\in \left[a,b\right),g\left(x\right)f\text{or}x\in \left(b,c\right]$ if f(b) =g(b) then

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