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2 years ago

For all values of x, f(x)=x-1 and g(x)=2x^2+3. Solve fg(x)=gf(x)

Mathematics

1 answer:

Phantasy [73]2 years ago

6 0

Answer:

x=3/4

Step-by-step explanation:

Given:

f(x) = x-1

g(x) = 2x²+3

Evaluate composite functions:

f(g(x)) = f(2x²+3) = (2x²+3)-1 = 2x²+2

g(f(x)) = g(x-1) = 2(x-1)²+3 = 2(x²-2x+1)+3 = 2x²-4x+2+3 = 2x²-4x+5

Set expressions equal to each other and solve for x:

2x²+2 = 2x²-4x+5

2 = -4x+5

-3 = -4x

3/4 = x

x = 3/4

Therefore, the value of x=3/4 satisfies both composite functions

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Does anyone know how to do this help please

statuscvo [17]

Answer:

$\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}$

Step-by-step explanation:

A quadratic function is given to us . And we need to fill out the table by using the function . The given function is ,

$\rm\implies y = x^2+x - 6$

Here we need to substitute the different values of x , to get the different values of y.

Put x = -3 :-

$\rm\implies y = 3^2-3-6\\$

$\rm\implies y = 9 - 3 - 6 \\$

$\rm\implies y = 0$

Put x = -2 :-

$\rm\implies y = 2^2-2-6\\$

$\rm\implies y = 4 -2-6\\$

$\rm\implies y = -4$

Put x = -1 :-

$\rm\implies y = -1^2-1-6\\$

$\rm\implies y = 1 -1-6 \\$

$\rm\implies y = -6$

Put x = 1 :-

$\rm\implies y = 1^2+1-6\\$

$\rm\implies y = 2 -6$

$\rm\implies y = -4$

Put x = 2 :-

$\rm\implies y = 2^2+2-6\\$

$\rm\implies y = 4 +2-6\\$

$\rm\implies y = 2$

Put x = 3 :-

$\rm\implies y = 3^2+3-6\\$

$\rm\implies y = 9 +3-6\\$

$\rm\implies y = 6$

Final table :-

$\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}$

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2 years ago

A candle burns down at the rate of 0.75 inches per hour. The original height of the candle was 9 inches.

VashaNatasha [74]

Answer:

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2 years ago

Which of the following is an example of a subset? The number of IT employees out of all employees working in an office of Google

marta [7]

Answer:

The number of IT employees out of all employees working in an office of Google

Step-by-step explanation:

The answer is the first one, because the rest Just describes a group of People, a subset is a part of a larger group of related things, while the others describes just a group of people, the first one which is the answer describes a group of people that's part of a larger group of people,

The subset is the IT employees working in an office for Google

whIle the main set is All employees working in an office of Google

4 0

2 years ago

Can enyone answer this question plz what is 10x4x5x2x34x89x73x3217x56=?

Molodets [167]

The answer is-- 15,918,086,598,400. why do you need it?

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3 years ago

Read 2 more answers

5. Walker is reading a book that is 792 pages. He reads

masya89 [10]

<h2>Forming Equations from Word Problems</h2>

To form equations from word problems, we can derive mathematical operations as well as variables from the given information.

In this case, each time Walker reads a certain number of pages, we subtract that from the total number of pages left to know how many pages is left to read.

<h2>Solving the Question</h2>

Let r represent the pages left to read.

792 pages in total

⇒ r = 792

Walker reads 15 pages a day during the week and 25 pages a day during the weekend.

There are 5 weekdays, and he reads 15 pages each of those days. ⇒ r = 792 - 5×15

There are 2 weekend days, and he reads 25 pages each of those days.
⇒ r = 792 - (5×15 + 2×25)

5 weeks have passed

Multiply the terms representing the number of pages he reads a week by 5, for 5 weeks.
⇒ r = 792 - (5×15 + 2×25)×5

<h2>Answer</h2>

r = 792 - (5×15 + 2×25)×5

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1 year ago