Did Cherise use algebra tiles to correctly represent the product of (x – 2)(x – 3)?
2 answers:
You might be interested in
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.
___
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.
__
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.
_____
The attached graph shows the inverse relation (called f₁(x)). It also shows a vertical line intersecting that graph in more than one place.
Step-by-step explanation:
Hope it helps.
Handwriting is a bit poor. So, restraint is advised!
:)
