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 .

Question

bmisses bmisses

04-12-2017
Mathematics

contestada

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 .

Respuesta :

Otras preguntas

What is the main difference between the right side and left side of the heart?

During an investigation, a student determines that a copper sample has a density of 8.10g/mL. What is the student's percent error if the a ccepted density for c

which accurately describes a tangent

What are the positive and negative aspects of a zoo or safari park?

The length of an arc of a circle is equal to 1/5 of the circumference of the circle. If the length of the arc is 2π, the radius of the circle is

which accurately describes a tangent

Lauren bought 20 ounces of sliced ham. she used 3/4 of the ham to make sandwiches for her friends and 1/5 of the ham in an omelet. how many ounces of ham were l

What is the biggest cause of extinction today? a. pollution b. exotic species c. global warming d. habitat loss

Lauren bought 20 ounces of sliced ham. she used 3/4 of the ham to make sandwiches for her friends and 1/5 of the ham in an omelet. how many ounces of ham were l

Why did the Chinese peasants rebel against the manchus from 1850 to 1864?

sarkhan2018 sarkhan2018 · Answer 1 · 2018-12-17T18:04:05+01:00

Answer:

The correct answer is B.

Step-by-step explanation:

In order to solve this problem, it is recommended to draw the graphs of the functions. By this way, you could easily observe the results.

By giving to [tex]x[/tex] - domain of the function different numbers, you can get the complete picture of each function.

One fact has to be mentioned that the domain of [tex]y=4^{x}[/tex] could be anything (all real numbers). However, the domain of logarithmic function cannot have negative numbers and 0.

When finally we draw the functions of the graphs, we'll get the following result in the picture.

[tex]y=4^{x}[/tex] is drawn with the red line, logarithmic function is drawn with the blue line and [tex]y=x[/tex] is drawn with the green line. The latter is used as an answer for the question where it shows that [tex]y=x[/tex] creates a symmetry for the functions.

tardymanchester tardymanchester · Answer 2 · 2019-04-29T07:39:16+02:00

Answer:

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 [tex]y=4^x[/tex] and [tex]y=\log_4x[/tex]

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

Solution :

Let, [tex]f(x)=4^x[/tex] and [tex]g(x)=\log_4x[/tex]

First we test whether two functions are inverse or not.

Condition for inverse: [tex]f(g(x))=g(f(x))=x[/tex]

[tex]4^{g(x)}=\log_4(f(x))[/tex]

[tex]4^{\log_4x}=\log_4(4^x)[/tex]

Applying law of logarithm and exponents,

[tex]x=x[/tex]

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.