Find [g o h](x) and [ h o g] 1. g(x)=x-6 h(x)=x+6 2. g(x)=x-3 h(x)=x^2 3. g(x)=x+2 h(x)=2x^2-3

g-o-hx-and-h-o-g

#1

Find g o h and [ h o g] 1. g(x)=x-6 h(x)=x+6 2. g(x)=x-3 h(x)=x^2 3. g(x)=x+2 h(x)=2x^2-3

Answer:

g o h and h o g are composite functions so the second term is a function of the first so without a given value to use you can just plug in the second equation for x in the first equation (in the first function term listed x is equal to x as the function of the second term listed).

  1. g o h=(h(x))-6; =(x+6)-6; plug the second function into the first (h(x) into x in g(x)) for x, then simplify; g o h=x
    h o g= (g(x))+6; =(x-6)+6; plug the second function into the first (g(x) into x in h(x)) for x, then simplify; h o g=x
  2. g o h= (x^2)-3; plug in and simplify(no more simplification possible); g o h=x^2 -3
    h o g= (x-3)^2; plug in and simplify; =(x-3)(x-3) (; I am assuming you know the foil process); h o g=x^2-6x+9
    3.g o h= (2x^2 -3)+2; plug in and simplify; g o h= 2x^2 -1
    h o g= 2(x+2)^2 -3; plug in and simplify; =2(x+2)(x+2)-3; =2x^2 +8x+8-3;
    h o g= 2x^2 +8x+5