f(x)= x^2+3x-5; g(x)=4-x

Question

• find the g-f 
• find fg
• find (g•f)(-1)
• find (f•g)(x)

Answer 1

f(x)= x^2+3x-5; g(x)=4-x find g-f
find the g-f ; find fg; find (g•f)(-1); and find (f•g)(x)

 

solution:  g - f = (4 - x) - (x^2 + 3x - 5)

                     =  - x^2 - x - 3x + 4 - (-5)

                     =  - x^2 - 4x + 9

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fg = (x^2 + 3x - 5)(4 - x) = distribute

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(g.f)(-1) = g(f(-1)) = g(1-3-5) = g(-7)

             = 4 - (-7) = 11

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(f.g)(x) = f(g(x)) = f(g) = g^2 + 3g - 5

            = (4 - x)^2 + 3(4 - x) - 5 = .....

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