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# Compositions

### Composition of functions

Question | Answer |
---|---|

If f(x)=x^2-8 and g(x)=3x find 1. (f+g)(x) | Simply plug in your f(x) which is: x^2-8 and do the same with your g(x). After plugging them both in simplify the answer. Answer: (f+g)(x) = x^2+3x-8 |

If f(x)=x-6 and g(x)=2x+7 find 1. (f-g)(x) | Just like the previous example you do the same exact thing but instead of adding the two functions you subtract them. Answer: (f-g)(x)=-x-13 |

If f(x)=x^2-8 and g (x)=3x find 1. (f * g)(x) | The steps are the same for this question but it requires ,multiplication. Answer: 3x^3-24x |

If f(x)=x-6 and g (x)=2x+7 find (f/g)(x) | By now it should be fairly simple, for this problem you plug in the functions. Answer: x-6/2x+7 |

If f(x)=x^2-8+3 and g (x)=-3x find the following composition. (f of g)(3) | (f of g)= 81+72 +3= 156 Answer:156 |

If g(x)=-9, h(x)=square root of x, find the composition. ( g of h)(0) | By substituting the functions the answer will be 0. Answer: 0 |

Find (f of g)(x) and (g of f)(x) f(x)= abs x, g(x)=8x-10 | Answer: (f of g)(x)= abs 8x-10 g(abs x)= 8 abs x -10 |

If f(x)= square root of x and g (x)=3x +7 find (f of g)(x) and (g of f) (x) | Answer: (f of g)(x)= square root 3x+7 (g of f)(x)= 3 square root x +7 |

If f(x)=6x, g(x)=square root of x and h(x)=x^2+10, write H(x)= square root of x^2+10 as composition using two of the given functions. | For this problem you would have to look at which function corresponds. Answer: H(x)=(g of h)(x) |

Let g(x)=x-10 find f(x) so that h(x)=(f of g)(x) h(x)=(x-10)^2 | Answer: f(x)=x^2 |

Refresh Question: If f(x)^2=x^2+10 and g(x)=6x, find a. (f+g)(x) b. (f-g)(x) c.(f*g)(x) d.(f/g)(x) | Answers: a. x^2+6x+10 b.x^2-6x+10 c. 6x^3+60x d. x^2+10/6x |