Function f and g are defined by f(x)=sqrt((x^2-2x)) and g(x)

Caroline Elliott

Caroline Elliott

Answered question

2022-01-22

Function f and g are defined by f(x)=(x22x) and g(x)=3x+4. The composite function is undefined for x]a;b[ . Find the value of a and b?

Answer & Explanation

kovaje5w

kovaje5w

Beginner2022-01-23Added 4 answers

The functions are
f(x)=x22x
g(x)=3x+4
The composite function is
f(g(x))=f(3x+4)
=(3x+4)22(3x+4)
=9x2+24x+166x8
=9x2+18x+8
The domain is
9x2+18x+80
Therefore,
The solution to this quadratic equation is
x=18±18249818
=18±18249818
=18±3618
=18±618
Therefore,
the composite function is undefined for
(2418,1218)
=(43,23)

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