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
How many numbers multiple of 3 are in the range [2,2000]?
amm1812

Answer: so there are 666 multiples of 3 between 2 and 2000.

Step-by-step explanation:

the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666

multiples of 3 between {2,2000} = 666-1+1 = 666

7 0
3 years ago
Jose has 4 friends and 3 apples how much would each friend get if he shared
blsea [12.9K]

\bf \cfrac{\stackrel{\textit{total amount of apples}}{3}}{\stackrel{\textit{total amount of people}}{4}}\qquad \qquad \quad\stackrel{Jose}{ \cfrac{3}{4}}+\stackrel{friend}{\cfrac{3}{4}}+\stackrel{friend}{\cfrac{3}{4}}+\stackrel{friend}{\cfrac{3}{4}}=\cfrac{12}{4}=3

5 0
3 years ago
Read 2 more answers
THIS IS URGENT I NEED HELP ASAP.(9x 10^-3)^2
joja [24]

(9x 10^-3)^2=\frac{81x^{2}}{1000000}, so d 8.1x10^-6

Evaluate 1/2a^-4b^2 for a =-2 and b=4

\frac{1}{2} (-2)^{-4} *4^{2}\\\\\frac{1}{2} *\frac{1}{(-2)^{4}} *4^{2}\\\\\frac{1}{2} *\frac{1}{2^{4}}*4^{2}\\\\\frac{1}{2} *\frac{1}{16}*4^{2}\\\\\frac{1}{2} *\frac{1}{16}*16=\frac{1}{2}

A number raised to a negative exponent is sometimes negative.

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)  

- Cutiepatutie ☺❀❤

8 0
3 years ago
Can someone help me on problem number 8?
kramer
List the coordinates,
Coordinates are shown as (x,y) 
If 2+2+7+7 is 16
You make those your side lengths 
Coordinates are (9,7) (2,7) (2,5) (9,5) 
they maybe slightly off because of the broken peice of paper
8 0
3 years ago
What is the factored form of 9X^2-64
Maksim231197 [3]
This should be recognized as the difference of perfect squares which is of the form:

(a^2-b^2) and the difference of squares always factors to:

(a-b)(a+b)  in this case:

(3x-8)(3x+8)
8 0
3 years ago
Read 2 more answers
Other questions:
  • I am doing a project in my math class where we create a picture with functions and needed an egg curve. I finally figured out th
    12·1 answer
  • Determine whether each set of side lengths could be the sides of a right triangle.
    12·1 answer
  • When simplified, (2x + 3)(7x – 1) + (2x – 4) is:
    12·1 answer
  • The dimensions of a 60 inch television set are approximately 52.28 inches wide and 29.42 inches high. What's the simplified rati
    6·2 answers
  • What is -7 divided by 1/2?
    10·2 answers
  • Evaluate f(x) = 2x at x = 5.<br> A) 32<br> B) 10<br> C) 64<br> D) 25
    11·1 answer
  • Find the polynomial. (2y − 9)(2y − 9) is the factored form of the expression
    9·2 answers
  • Help mw with tis qustion
    5·2 answers
  • Need help asap pleas and thank you .
    9·1 answer
  • PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!