find the following for the given equations

Question

A. (f ° g) B. ( g ° f) (x) 

 

3x²-5 and g(x)= √4x+7 

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find the following for the given function 

f(x)=2x²-7x and g(x)=3x+8

a)(f+g)

b)(f-g)(-2)

c)(f•g)(-4)

d)(f/g)(-1)

Answer 1

Oh Jennifer

 

Note that g(x) = 2X + 7

 

a) f(g(x)) = 3 [ 2X + 7 ]^2 - 5

               = 3 [ 4x^2 + 28 X + 49]- 5

               = 12X^2 + 84X + 147 - 5

               = 12X^2 + 84X + 142

 

b) g(f(x)) = 2( 3X^2 - 5) + 7

               =  6x^2 - 10 + 7

              = 6x^2 - 3

 

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a) f + g = 2x2 - 4x + 8

b) f - g = 2X^2 - 10X - 8 , so at X=-2 the result is 2(-2)^2 - 10(-2) - 8 = 2*4 + 20 - 8 = 8 + 20 - 8 = 20

c) f*g = 6x^3 - 21x^2 + 16X^2 - 56X = 6X^3 - 5x^2 - 56x = x(6x^2 - 5X - 56)

      so at X=-4, the result is -4( 6*(-4)^2 - 5(-4) - 56) =

                                         -4( 6*(16) + 20 - 56) =

                                         -4( 96 + 20 - 56) =

                                         -4( 60) = -240

 

d) f/g = (2X^2-7X)/(3X+8)  so for X=-1, the result is (2(-1)^2 - 7(-1))  / (3*-1 + 8)

                                                      = (2(1) + 7)/( -3 + 8) =

                                                         (2 +7)/(-3+8) = 9/5 = 1.4