15 cm 21 cm 28 cm 42 cm Calculate the greatest possible area of the shaded region.
1 answer:
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Answer:
Step-by-step explanation:
To find the inverse function, solve for y:
f(x) is an even function, so f(-x) = f(x). Then the inverse relation is double-valued: for any given y, there can be either of two x-values that will give that result.
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A function is single-valued. That means any given domain value maps to exactly one range value. The test of this is the "vertical line test." If a vertical line intersects the graph in more than one point, then that x-value maps to more than one y-value.
The horizontal line test is similar. It is used to determine whether a function has an inverse function. If a horizontal line intersects the graph in more than one place, the inverse relation is not a function.
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Since the inverse relation for the given f(x) maps every x to two y-values, it is not a function. You can also tell this by the fact that f(x) is an even function, so does not pass the horizontal line test. When f(x) doesn't pass the horizontal line test, f^-1(x) cannot pass the vertical line test.
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The attached graph shows the inverse relation (called f₁(x)). It also shows a vertical line intersecting that graph in more than one place.
K is the slope of the line formed by connecting the points.
Use slope formula:
where the 2 points are the end points of the line (First and last going Left to right)
Substitute into slope formula
You can check if this is correct by going back to graph and going "up 7" and "over 2" to get from one point to the next.
Use slope formula:
where the 2 points are the end points of the line (First and last going Left to right)
Substitute into slope formula
You can check if this is correct by going back to graph and going "up 7" and "over 2" to get from one point to the next.