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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.

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Answer:

  No.

Step-by-step explanation:

The exponent of y is 2, which is not 1, so the equation is 2nd degree, <em>not linear</em> (1st degree).

6 0
3 years ago
WILL NAME BRAINLIEST
ehidna [41]

Answer:

The answer for a different question is 5x

Step-by-step explanation:

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7 0
3 years ago
4x2 + 9y2 = 72<br> 2x - y = 4<br><br> Which of the following is a solution to the system shown?
Ede4ka [16]
If you would like to solve the system of equations, you can do this using the following steps:

4x^2 + 9y^2 = 72
2x - y = 4 ... 2x - 4 = y
_________
<span>4x^2 + 9y^2 = 72
</span><span>4x^2 + 9 * (2x - 4)^2 = 72
</span>4x^2 + 9 * (4x^2 - 16x + 16) = 72
4x^2 + 36x^2 - 144x + 144 = 72
40x^2 - 144x + 144 - 72 = 0
40x^2 - 144x + 72 = 0
10x^2 - 36x + 18 = 0
5x^2 - 18x + 9 = 0
(5x - 3) * (x - 3) = 0
1. 5x - 3 = 0 ... 5x = 3 ... x = 3/5
2. x = 3

<span>1. y = 2x - 4 = 2 * 3/5 - 4 = 6/5 - 20/5 = -14/5
2. y = 2x - 4 = 2 * 3 - 4 = 6 - 4 = 2

1. (x, y) = (3/5, -14/5)
2. (x, y) = (3, 2)

The correct result would be </span>(3/5, -14/5) and <span>(3, 2).</span>
5 0
3 years ago
Factor the gcf out of the expression: -6x^3 - 9xy + 18x
Westkost [7]

Answer:

-207xy

Step-by-step explanation:

-6x^3 - 9xy + 18x

-216x -9xy +18x

-225xy + 18x

-207xy

If I'm not mistaken.

6 0
3 years ago
Which would be a good statistical question Alexandra could have used to create the tally chart?
Roman55 [17]

Answer: D

Step-by-step explanation:

Sorry I’m late.

Remember:

A STATISTICAL QUESTION has variable answers.

Ex: How many toys are in the U.S?

A NON-STATISTICAL QUESTIONS have only one answer

4 0
3 years ago
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