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
777dan777 [17]
3 years ago
6

Define a function f on a set of real numbers as follows: f(x) = 3x − 1 x , for each real number x ≠ 0 Prove that f is one-to-one

. Proof: Let x1 and x2 be any nonzero real numbers such that f(x1) = f(x2). Use the definition of f to rewrite the left-hand side of this equation. (Enter the answer as an expression in x1.) Then use the definition of f to rewrite the right-hand side of f(x1) = f(x2). (Enter the answer as an expression in x2.) Equate the expressions obtained for the left- and right-hand sides of f(x1) = f(x2), and simplify the result completely. The result is the following equation. x1 = Therefore, f is .
Mathematics
1 answer:
dalvyx [7]3 years ago
6 0

Answer with Step-by-step explanation:

We are given that

f(x)=\frac{3x-1}{x}

For each real number x\neq 0

To prove that f is one -to-one.

Proof:Let x_1 and x_2 be any nonzero real numbers such that

f(x_1)=f(x_2)

By using the definition of f to rewrite the left hand side of this equation

f(x_1)=\frac{3x_1-1}{x_1}

Then, by using the definition of f to rewrite the right hand side of this equation  of f(x_1)=f(x_2)

f(x_2)=\frac{3x_2-1}{x_2}

Equating the expression then we get

\frac{3x_1-1}{x_1}=\frac{3x_2-1}{x_2}

3x_1x_2-x_2=3x_2x_1-x_1

3x_1x_2-3x_1x_2+x_1=x_2

x_1=x_2

Therefore, f is one-to-one.

You might be interested in
Solve for x. (x - 4)(x - 4) = 0
statuscvo [17]
I believe that x=4 would be the answer
5 0
3 years ago
Read 2 more answers
Help, please! If possible explain it like your talking to a little kid :) Thank you♡
monitta

Answer:

GCF: y³z³

Step-by-step explanation:

The greatest common factor is the a term that you can take out of all the terms given to you. This term, when multiplied to each of the individual numbers in the set, will return you to the original amount.

In this case, note that they all share the variables y and z, and that each of them have <em>at least</em> 3 y's and 3 z's. For you to factor, you will divide these from all the terms.

\frac{x^{3}y^{5}z^{5} , y^{3}z^{5} , xy^{3}z^{3} }{y^{3}z^{3}} = x^{3}y^{2}z^{2} , z^{2} , x

y³z³(x³y²z² , z² , x)

~

7 0
2 years ago
Help pleasee
Mnenie [13.5K]
Let x be the amount of cement and y be the amount of sand. If <span>the ratio of cement to sand for mortar is 1:3, then \frac{x}{y} = \frac{1}{3} and y=3x.
</span>
So, if <span>Sandy puts in x=7 shovels of cement, then she puts y=3\cdot 7=21 shovels of sand.
</span><span>
</span><span>Answer: 21 shovels of sand.
</span>
6 0
3 years ago
Read 2 more answers
Hi i need help with this
ICE Princess25 [194]
The range would be [-4, infinity) because range is the y-value. The lowest y-value is -4. The greatest y-value goes up to infinity.
7 0
3 years ago
in a right triangle, the 58cm hypotenuse makes a 51 angle with one of the legs. rounded to two decimals places, how long is that
ser-zykov [4K]

Answer:

36.50

To two decimal places

Step-by-step explanation:

The hypothenuse side in a right angle triangle has 58cm. While the angle touching one of its leg is 51°. How long is that leg.

From the right angled triangle, the size of the leg touching the hypothenuse is the adjacent side of the triangle, hence in trigonometry, the cosine rule is used, because it involves the adjacent and the hypotenuse.

Cos 51°=x/58

Let the size of the leg be x

Making x the subject

x=58(Cos51°)

x=36.500058

Correct to two decimal place

x=36.50

3 0
3 years ago
Other questions:
  • Using a rain gauge, Gerry determined that 1/2 inch of rain fell during 3/4 of an hour. What is the unit rate of rainfall in inch
    11·2 answers
  • Use the quadratic formula to solve the equation.<br><br>-3x^2 - x - 3 = 0
    14·1 answer
  • Which number is prime 70 49 31 85
    5·1 answer
  • If your car gets 35 miles per​ gallon, how much does it cost to drive 400 miles when gasoline costs ​$3.30 per​ gallon?
    14·1 answer
  • Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at colleg
    14·1 answer
  • Which algebraic expression is equivalent to the expression below?
    7·2 answers
  • What line represents the relationship
    14·1 answer
  • 182 is what percent of 130?​
    15·1 answer
  • Shown are the number of baskets made by Mark in 10 basketball games-
    10·1 answer
  • What is the first step is 12 devided by 4 x 3 + 2 x 1
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!