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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We can use the Horizontal Line Test to determine whether the inverse of a function is also a function. If it is a function, $(f(x)$ is invertible. To do this with the given function, we will first make a table of values to graph it. When making a table of values, make sure to use a variety of points, including negative and positive values.

$x$ | $2x_{2}$ | $f(x)=2x_{2}$ |
---|---|---|

$-4$ | $2(-4)_{2}$ | $32$ |

$-3$ | $2(-3)_{2}$ | $18$ |

$-2$ | $2(-2)_{2}$ | $8$ |

$-1$ | $2(-1)_{2}$ | $2$ |

$0$ | $2(0)_{2}$ | $0$ |

$1$ | $2(1)_{2}$ | $2$ |

$2$ | $2(2)_{2}$ | $8$ |

$3$ | $2(3)_{2}$ | $18$ |

Now we can plot the obtained points and connect them with a smooth curve. Consider also that this is an even-degree polynomial with a positive leading coefficient. This tells us about the end behavior of the function. $ f(x)→-∞asx→+∞f(x)→+∞asx→+∞ $ Therefore, it will continue upward in both directions.

Finally, we can perform the Horizontal Line Test. If the horizontal lines intersect the graph once, then the inverse is also a function. Conversely, if there is even one horizontal line that intersects the graph more than once, then the inverse is **not** a function.

We can see above that there are horizontal lines that intersect the curve at more than one point. Therefore, the inverse of the given function is **not** a function. The function $f(x)$ is not invertible.