What is the minimum value of the function over the interval -5 < x < 5? h(x) = log[(x – 3)^2 + 2]

ln(2)

Step-by-step explanation:

In order to minimize ln[(x – 3)^2 + 2], we have to minimize [(x – 3)^2 + 2] since natural log is an increasing function

For that, it suffices to minimize (x – 3)^2, which is non-negative for all real numbers x

As such, the minimum value is achieved when x - 3 = 0; - 5 < 3 < 5

Substitute x = 3 in the original equation to get ln(2)

because 1.2 isnt half of 6 duh

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.