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For what value of x is gof(x) = fog(x) if f(x)=8x+12 and g(x)=3x-6.

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xetaalpha | Student | (Level 2) Honors

Posted June 20, 2011 at 3:49 AM via web

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For what value of x is gof(x) = fog(x) if f(x)=8x+12 and g(x)=3x-6.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 20, 2011 at 3:55 AM (Answer #1)

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We are given f(x) = 8x + 12 and g(x) = 3x - 6. We have to determine the value of x for which fog(x) = gof(x)

fog(x) = gof(x)

=> f(g(x)) = g(f(x))

=> f(3x - 6) = g(8x + 12)

=> 8(3x - 6) + 12 = 3(8x + 12) - 6

=> 24x - 48 + 12 = 24x + 36 - 6

=> -36 = 30

This is not possible.

fog(x) is not equal to gof(x) for any value of x.

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