If u=(fog)(x) and v=(gof)(x), verify if u'=v'? f(x)=3x+2,g(x)=x^2+1

Expert Answers

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We have the functions f(x) = 3x+ 2 and g(x) = x^2 + 1

u = fog ( x) = f(g(x))

=> f(x^2 + 1)

=> 3(x^2 + 1) + 2

=> 3x^2 + 3 + 2

=> 3x^2 + 5

v = gof(x) = g(f(x))

=> g( 3x + 2)

=> (3x + 2)^2 +1

=> 9x^2 + 4 + 12x + 1

=> 9x^2 + 12x + 5

u' = 6x

v' = 18x + 12

Therefore u' is not equal to v'.

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