Is the inverse of f(x)=x^2 is also a function true or false
1 answer:
Solution:
The given statement is False.
Explanation:
We have been given the equation
In order to check whether the inverse is a function or not, we can perform horizontal line test.
Horizontal line test:- If a horizontal line intersects the graph at more than one point then the inverse is not a function. If it intersects at exactly one point then the inverse is a function.
The given equation represents a upward parabola shown in the attached image. The vertex of the parabola is at origin.
Now, we draw a horizontal line and check the number of intersection point of the line and the parabola. We can see that the horizontal line intersects the parabola at two points.
Hence, from horizontal line test, the inverse is a not a function.
Therefore, the given statement is False.
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We are told that circle C has center (-4, 6) and a radius of 2.
We are told that circle D has center (6, -2) and a radius of 4.
If we move circle C's center ten units to the right and eight units down, the new center would be at (-4 + 10), (6 - 8) = (6, -2). So step 1 in the informal proof checks out - the centers are the same (which is the definition of concentric) and the shifts are right.
Let's look at our circles. Circle C has a radius of 2 and is inside circle D, whose radius is 4. Between Circle C and Circle D, the radii have a 1:2 ratio, as seen below:
If we dilate circle C by a factor of 2, it means we are expanding it and doubling it. Our circle has that 1:2 ratio, and doubling both sides gives us 2:4. The second step checks out.
Translated objects (or those that you shift) can be congruent, and dilated objects are used with similarity (where you stretch and squeeze). The third step checks out.
Thus, the argument is correct and the last choice is best.