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Use the functions below to answer the questions

g(x)=x^{2}-4x+2 f(x)=5x-9 h(x)=(1/4)x+6

- (h-f)(4)
- Find x if h(x)=9
- Find n if f(n)=f(3n+1)

Thanks

Guest Mar 21, 2018

#1**0 **

1. \((h-f)(4)=h(4)-f(4)\)

The left hand side and the right hand of the equation are equivalent. The notation on the right might be more intuitive, though.

\(h(4)-f(4)\) | Evaluation both functions when x equals 4. |

\(h(4)=\frac{1}{4}*4+6\) | Here, I have replaced all instances of an "x" with a 4. Now, let's evaluate h(4). |

\(h(4)=1+6=7\) | Now, let's find f(4). |

\(f(4)=5*4-9\) | Yet again, every appearance of "x" is replaced with the input, 4. |

\(f(4)=11\) | The original question wants you to subtract the two functions, so let's do that. |

\(h(4)-f(4)\\ 7\hspace{6mm}-\hspace{3mm}11\) | |

\(-4\) | |

2) If h(x)=9, then we can use substitution to find the value of x:

\(h(x)=\frac{1}{4}x+6\) | Replace h(x) with 9 since they are equal. |

\(9=\frac{1}{4}x+6\) | Subtract 6 from both sides of the equation. |

\(3=\frac{1}{4}x\) | Multiply by 4 on both sides to isolate the variable. |

\(x=12\) | |

3) If f(n)=f(3n+1), then we can evaluate both functions for the given input and set them equal to each other.

\(f(x)=5x-9\) | \(f(x)=5x-9\) | |

\(f(n)=5n-9\) | \(f(3n+1)=5(2n+1)-9\) | |

\(f(3n+1)=10n+5-9\) | ||

\(f(n)=5n-9\) | \(f(3n+1)=10n-4\) | |

As aforementioned, these values are equal, so let's set them equal

\(\hspace{4mm}f(n)=f(3n+1)\\ 5n-9=10n-4\) | Now, solve for n. Move the constants and linear terms over to one side of the equation. |

\(-5=5n\) | Finally, divide by 5. |

\(-1=n\) | |

TheXSquaredFactor Mar 22, 2018