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function and relation 1

Mathematics
Tutor: None Selected Time limit: 0 Hours

1.) find f(x)) if f(x)=3x+1 and g(x) = x squared -1 

2.) find g(f(x)) if f(x) = 2x-3 and g(x) = x squared -1

3.) what is f(-4) for f(x)= x+4/2?

4.) find (f+g)(x) if f(x)=1/2x+4 and g(x) =-x-3

5.) find g(f(x)) if f(x) =-6+10 and g(x)=3x-2

Sep 16th, 2014

1. Find   f(g(x)) 

=f(x² -1)

= 3(x² -1)+1

= 3 x² -3 +1

= 3 x² -2

2. g(f(x))

= g (2x-3)

= (2x-3)² -1

=4x²-12x +9 -1

= 4x²-12x +8

3. f(x)= (x+4)/2

  f(-4) = (-4+4)/2     (substitute x=4 into formula for f(x)

        =0/2

         =0

4. (f+g)(x) =f(x) + g(x)

                   =1/2x +4 + -x-3

                   =-1/2x +1

5. find g(f(x)) if f(x) =-6x+10 and g(x)=3x-2

g(f(x)) = g(-6x+10)

           = 3 (-6x+10) -2

           = -18x +30 -2

           = -18x +28

(There were some mistakes in your questions which I hope I have correctly written)


Sep 16th, 2014

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