Which statements represent the relationship between y=4x and y=log4x ? select each correct answer. a. the functions are inverses of each other. b. the graphs of functions are symmetric to each other over the line y = x. c. the graphs of functions are symmetric about the line y = 0. d. the equation y=log4x is the logarithmic form of y=4x .

Option a and b

a. The functions are inverses of each other.

b. The graphs of functions are symmetric to each other over the line y = x.

Step-by-step explanation:

Given : Equation and              

To find : Which statements represent the relationship between  two equations?

Solution :

Let,   and      

First we test whether two functions are inverse or not.

Condition for inverse:                        

Applying law of logarithm and exponents,

So the two functions are inverses of each other.

The function and its inverse are always symmetrical about the line:  y=x

Therefore, Option a and b are correct.    

Refer the attached figure below.