Function f and g are defined by f(x)=(x2−2x) and g(x)=3x+4. The composite function is undefined for x∈]a;b[ . Find the value of a and b?

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kovaje5w · Accepted Answer

The functions are  f(x)=x2−2x  g(x)=3x+4  The composite function is  f(g(x))=f(3x+4)  =(3x+4)2−2(3x+4)  =9x2+24x+16−6x−8  =9x2+18x+8  The domain is  9x2+18x+8≥0  Therefore,  The solution to this quadratic equation is  x=−18±182−4⋅9⋅818  =−18±182−4⋅9⋅818  =−18±3618  =−18±618  Therefore,  the composite function is undefined for  (−2418,−1218)  =(−43,−23)

Function f and g are defined by f(x)=(x2−2x) and g(x)=3x+4. The composite function is undefined...

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