What is the inverse of the function below?

The answer is:

The correct option is:

c)

Inversing a function means switching the range and domain of the function. To inverse a function we need to rewrite the variable (x) with the function (f(x) or y), and rewrite the function (f(x) or y) with the variable (x), and then, isolate "y" or "f(x)".

Also, we need to remember how to isolate the variable from a logarithmic function.

So, we are given the function:

Which it's equal to write:

Then, inversing the function we have:

Hence, we have that the correct answer is the option:

c)

Have a nice day!

8

step-by-step explanation:

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'.