Can someone help me solve for x?
1 answer:
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Answer:
- inverse is not a function
- unless the domain is restricted to |x| ≥ 1.2 (approximately)
Step-by-step explanation:
The test to see if the inverse function is also a function is called the "horizontal line test." The test passes if any horizontal line intersects the graph in only one place.
Here, a horizontal line can intersect the graph in 1, 2, or 3 places, so the test fails. The function does not have an inverse that is a function.
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If the domain of the inverse relation is restricted to |x| > 1.2, then that inverse will map any x to only a single value of y. Then it will be a function.
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The graph shows the original function (dashed red line) and the inverse relation (blue). The green shading marks values of x for which there is a single value of y, so the inverse relation is a function in those regions.
(We could be more specific as to the limits on the domain of f^-1(x), but the given graph seems to have an unknown vertical scale factor.)
