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3 years ago

If f(3x − 1) = 6x − 1, find f(x) and f(0)

Mathematics

1 answer:

klio [65]3 years ago

5 0

f(3x - 1) = 6x - 1

Rewrite 6x - 1 as a function of 3x - 1:

6x - 1 = 6x - 2 + 1 = 2(3x - 1) + 1

That is,

f(3x - 1) = 2(3x - 1) + 1

which means

f(x) = 2x + 1

and so

f(0) = 2*0 + 1 = 1

You might be interested in

78% of the class completed their homework last night. What fraction of the class completed their homework?

mixas84 [53]

Answer:

$\frac{39}{50}$

Step-by-step explanation:

=> 78% makes:

=> $\frac{78}{100}$

<u><em>In simplest form:</em></u>

=> $\frac{39}{50}$

3 0

3 years ago

Read 2 more answers

Sales of 10000 increased by 65% each year write a function that represents the situation

erastovalidia [21]

Answer: $y=10000(1.65)^x$

Step-by-step explanation:

Given: The sales of 10000 increased by 65% each year .

Let x be the number of years.

The rate of growth=65%= 0.65

The exponential growth function is given by

$y=A(1+r)^x$

, where A is initial amount and r is the rate of growth in decimal.

Then the increase in the sales id given by :-

$y=10000(1+0.65)^x\\\Rightarrow\ y=10000(1.65)^x$

6 0

3 years ago

Explain how to compute 3/4 x 4/5 using one diagram.

Drupady [299]

Answer:

The simplified form of given expression is 3/5.

Step-by-step explanation:

The given expression is

$\frac{3}{4}\times \frac{4}{5}$

We need to find the product of two factions using diagram.

For 3/4, draw a box and divide it in 4 equal parts by using vertical lines. The color three parts of it.

For 4/5, draw a box and divide it in 5 equal parts by using horizontal lines. Then color the four parts of it.

Now combined both boxes and shown below.

From the below figure it is clear that

The number of common shaded small boxes = 12

Total number of small boxes = 20

The required fraction is

$Fraction=\frac{\text{Number of common shaded small boxes}}{\text{Total number of small boxes}}$

$Fraction=\frac{12}{20}$

Cancel out common factor.

$Fraction=\frac{3}{5}$

Therefore, the simplified form of given expression is 3/5.

5 0

3 years ago

ANSWER QUICKLY!!!!!

Paul [167]

Answer:

1. The possible roots are ±1, ±2, ±3, ±6. These are the factors of the trailing constant (6) divided by the factors of the leading coefficient (1). When the leading coefficient is 1, the possible roots are the factors of the constant

2. The polynomial is easier to evaluate when it is written in Horner form:

f(x) = ((x -4)x +1)x +6

To show that 2 is a zero, we want to find f(2):

f(2) = ((2 -4)2 +1)2 +6 = (-4 +1)2 +6 = -6 +6 = 0

f(2) = 0, so 2 is one of the zeros of this function

3. Using synthetic division (attached) or polynomial long division, we can divide the given polynomial by (x-2) to find the remaining factors. This division gives (x^2 -2x -3), which can be factored as (x -3)(x +1), so the three actual roots are ...

x = 2 (from above), x = 3, x = -1 (from our factorization)

4. In factored form, the polynomial can be written ...

f(x) = (x +1)(x -2)(x -3)

The first factor was found from the fact that 2 was given as a zero of the function. For any zero "a", a factor of the polynomial is (x-a).

The remaining factors were found by factoring the quadratic trinomial that resulted from the division of f(x) by x-2. That trinomial is x^2 -2x -3.

There are a number of methods that can be used to factor x^2 -2x -3. Again, the rational root theorem can help. It suggests that ±1 and ±3 are possible roots.

4 0

2 years ago

There are 143076 books in the library. The 3rd grade class walked over and each kid checked out 2 books. There are 21 students i

9966 [12]

Answer:

The answer is: There are only 143034 books left after the students return to their classroom

Step-by-step explanation:

Lets call X= Number of books left in the library after the students return to their classroom.

B=Total of Books in the library

S=Total of books taken by the 3rd grade students

If each student of the 3rd grage class take 2 books, the total of book taken by the 3rd grade students would be:

S=2 books per student * Total of students of the 3rdgrade

S=2*21=42

Then we must substract Total of Books in the library minus Total of books taken by the 3rd grade students. That would be:

X=B-S

X=143076-42

X=143034

I hope that this answer will help you

7 0

3 years ago