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# Module 21

### Math 113

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

How do you find the inverse of a one-to-one function? | By switching the coordinates of the ordered pairs of the function. |

What is one important thing to remember when working with subtracting Algebraic functions? | It is important to distribute the negative sign to the entire problem. It is one of the easiest mistakes that happens when working with functions. |

What are the two symbols to look out for when solving the function operations? | Remember not to get the dot used for multiplication mixed up with the circle used for the operation of composition. |

What is something you should never forget to do when you are done solving composite functions? | It is essential that you go over the problem, which is important for any type of equation. However, you should really focus on whether or not the problem is in the correct order. |

What is the Algebra of Functions? | This is finding the sum, difference, product, and quotient of functions to generate new functions. |

What is the relationship between graphs of functions and graphs of sums, difference, product, and quotients? | You are able to add these graphs together adding the y-values of the corresponding x-values. |

g(f(x)) means? | it means g composed with f. |

f(g(x)) means? | it means f composed with g. |

If f(x)=x-1 and g(x)=-2x-3 find (f+g)(x) | (f+g) also equals f(x) plus g(x) Simply add the two functions. (x-1)+(-2x-3)=(3x-4) |

If f(x)x-1 and g(x)=-2x-3 find (f-g)(x) | (f-g) also equals f(x) minus g(x) Make sure that you distribute the minus sign to the entire second function. The new function will be (2x+3) (x-1)-(-2x-3)=-x+2 |

If f(x)=x-1 and g(x)=-2x-3 find (f/g)(x) | (f/g) also equals f(x) over g(x) if g is not equal to 0. Simply divide here. (x-1)/(-2x-3)=3/2 |

If f(x)=x-1 and g(x)=-2x-3 find (f•g)(x) | (f•g) also equals f(x) times g(x) Use the FIFO method when solving this function. (x-1)(-2x-3)equals 2x^2-5x+3 |

Given f(x) = 2x + 3 and g(x) = –x2 + 5, find ( f o g)(x). | the key here is to identify the sign of composition. Next, work inside out.f(g(x) ( f o g)(x) = f (g(x)) = f (–x2 + 5) = 2( ) + 3 = 2(–x2 + 5) + 3 = –2x2 + 10 + 3 = –2x2 + 13 |

Given f(x) = 2x + 3 and g(x) = –x2 + 5, find (g o f )(x). | (g o f )(x) = g( f(x)) f(g(x)) = g(2x + 3) = –( )2 + 5 ... = –(2x + 3)2 + 5 = –(4x2 + 12x + 9) + 5 = –4x2 – 12x – 9 + 5 = –4x2 – 12x – 4 |

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