1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
iren2701 [21]
3 years ago
6

True or false (Picture provided)

Mathematics
2 answers:
STatiana [176]3 years ago
7 0

Answer:

False.

Step-by-step explanation:

We have given a function and its inverse:

f(x) = (x-3)³+4  and    f⁻¹(x) = -3+∛ (x+4)

We have to find is it inverse of function or not.

We have given a function:

f(x) = (x-3)³+4

let f(x) = y we get,

y = (x-3)³+4

Interchange the place of x and y we get,

x= (y-3)³+4

(y-3)³ = x-4

y-3 = ∛ x-4

y = ∛ x-4 +3

Replacing y to f⁻¹(x)  we get,

f⁻¹(x) = ∛ x-4 +3

The inverse of given function is f⁻¹(x) = ∛ x-4 +3.Which is different from the given inverse.

So, it is false.

aksik [14]3 years ago
3 0
<h2>Answer:</h2><h3>False</h3><h2>Step-by-step explanation:</h2>

Let's find the inverse function of f(x)=(x-3)^3+4 to know whether this function has an inverse function f^{-1}(x)=-3+\sqrt[3]{x+4}. So let's apply this steps:

a) Use the Horizontal Line Test to decide whether f has an inverse function.

Given that f(x) is a cubic function there is no any horizontal line that intersects the graph of f at more than one point. Thus, the function is one-to-one and has an inverse function.

b) Replace f(x) by y in the equation for f(x).

y=(x-3)^3+4

c) Interchange the roles of x and y and solve for y

x=(y-3)^3+4 \\ \\ \therefore x-4=(y-3)^3 \\ \\ \therefore (y-3)^3=x-4 \\ \\ \therefore y-3=\sqrt[3]{x-4} \\ \\ \therefore y=\sqrt[3]{x-4}+3

d) Replace y by f^{-1}(x) in the new equation.

f^{-1}(x)=\sqrt[3]{x-4}+3

So this is in fact the inverse function and it isn't the same given function. Therefore, the statement is false

You might be interested in
Please help meeeeeeeeeee
rodikova [14]

8-5=3 : This means you add three each time

f(5)=8+3=1

f(6)=11+3=14

hope this helps :)

if not snap chat has a feature in the search bar and you can get answers by that

4 0
3 years ago
I need help with a math problem 6838 multiplied by 2830 then that answer divided by 2
Tresset [83]

Answer:

9675770

Step-by-step explanation:

Hope this helps

7 0
3 years ago
Read 2 more answers
The total area of both plots of land is?
VikaD [51]

You have 2x^2 + 9x -9 and 3x^2 -2x +14

To find total area add the two polynomials together by combining the like terms.


2x^2 + 3x^2 = 5x^2

9x + -2x = 9x-2x = 7x

-9 + 14 = 5


Total area = 5x^2 + 7x + 5

7 0
3 years ago
Help me please I all ready submit all my question on my profile go see it it is due right now I will mark you as a brainlest rig
pashok25 [27]

Answer:

ok

Step-by-step explanation:

6 0
3 years ago
(-5, -1, 10, -9)<br> on the number line.
lbvjy [14]
-9,-5, -1, 10 is the right order
4 0
2 years ago
Other questions:
  • The minute hand of a clock is six (6) inches long. a. How far does the tip of the minute hand move in 24 hours? Write your answe
    9·1 answer
  • Idk how to do this stuff so plz help
    15·1 answer
  • Classify the statement as either true or false.
    7·1 answer
  • A $3,000 loan is taken out for 9% interest for 6 months. What is the amount of interest charged?
    11·2 answers
  • What is the arithmetic mean of the following numbers?<br> 8, 10, 10, 10,6,7,8
    7·1 answer
  • Help me with this please<br> only number 13 &amp; 14
    15·2 answers
  • Each big square below represents one whole.
    8·1 answer
  • Roxanne ran 10.73 miles on Monday and 3.01 miles on Tuesday. How many more miles did Roxanne run on Monday than Tuesday?
    12·1 answer
  • Please help!! Need an explanation by tomorrow and I am super confused!
    11·1 answer
  • Please help ASAP!! Conner and Jana are multiplying (3⁵6⁸)(3⁹6¹⁰).
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!