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Example 1
Function f has its graph completely in Quadrant $III$. Where will the graph of the inverse function of $f$ be?
- $IV$
- $II$
- $I$
- $III$
- $I$ and $II$
Solution
- According to the 5 possible answers, we are looking for a quadrant.
- By definition of the inverse function if $(a,b)$ is a point on the graph of $f$, then the point $(b,a)$ is on the graph of its inverse.
- To find in which quadrant is a point located, we need to find the signs of its coordinates. If the graph of is in quadrant $III$, then both coordinates $a$ and $b$ are negative. Hence the point $(b,a)$ on the graph of the inverse also has both coordinates negative and therefore the graph of the inverse is located in quadrant $III$.
Answer D
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