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Given f(x) = |x − 2| and g(x) = 3/(​x^2 + 2)

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Given f(x) = |x − 2| and g(x) =3/(x2 + 2)

, find the following:
a. f[f(1)] b. g[f(2)] c. f[g(4)] d. g[g(0)] 

asked Dec 24, 2017 in ALGEBRA 1 by anonymous

1 Answer

0 votes

The functions are

f(x)   =   |x - 2|

g(x)   =   3 / (x^2 + 2)

 

f(1)   =  | 1 - 2 |

        =  | - 1|

f(1)  =  1

 

f(2)   =  | 2 - 2 |

        =  | 0 |

f(2)  =  0

 

g(4)   =   3 / (4^2 + 2) 

         =   3 / (16 + 2)

         =   3 / 18

g(4)   =   1/6

 

g(0)  =  3/ (0^2 + 2)

g(0)   =   3/2

 

a)

f[f(1)]   =   f(1)

           =  | 1 - 2 |

           =  | - 1|

f[f(1)]   =  1

 

b)

g[f(2)]   =   g(0)

               =   3/(0^2 + 2)

g[f(2)]   =   3/2

 

c)

f[g(4)]   =   f(1/6)

            =    | (1/6) - 2 |

            =    | (1 - 12)/6 |

            =    | - 11/6 |

f[g(4)]   =   11/6

answered Dec 24, 2017 by homeworkhelp Mentor

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