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levacccp [35]
2 years ago
11

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:

<u>Given:</u>

f(x) = x-1

g(x) = 2x²+3

<u>Evaluate composite functions:</u>

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

<u>Set expressions equal to each other and solve for x:</u>

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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HELP HELP !! &amp; PlEASE SHOW WORK ! What would be the compound interest rate if Tom borrowed $6,000 at a 3% interest rate for
In-s [12.5K]

Answer:

Compound interest = $365.4

Step-by-step explanation:

Given:

Amount borrowed = $6,000

Rate of interest = 3%

Number of year =  year

Find:

Compound interest

Computation:

A = P[1+r]ⁿ

Amount after 2 year = 6,000[1 + 3%]²

Amount after 2 year = 6,000[1 + 0.03]²

Amount after 2 year = 6,000[1.03]²

Amount after 2 year = 6,000[1.0609]

Amount after 2 year = 6,365.4

Compound interest = Amount after 2 year - Amount borrowed

Compound interest = 6,365.4 - 6,000

Compound interest = $365.4

3 0
2 years ago
Julius is buying beverages for brunch. He needs to buy a total of 5
xeze [42]
Well, he only needs 5 gallons of beverages. Because he buys two containers of each, however, that means he bought 320 gallons total (I would say). How I got my answer:

There are 8 pints in a gallon (8 x 2)
There are 4 quarts in a gallon (4 x 2)
There are 16 cups in a gallon (16 x 2)
There are 128 ounces in a gallon (128 x 2)

With that being said, we can add these to find the total amount of gallons of beverages Julius bought. 16 + 8 + 8 + 32 + 256 = 320.

Hopefully this helps!
7 0
2 years ago
Which number can be inserted in the parentheses to make the statement true? negative 3 and one-fourth is greater than left-paren
DIA [1.3K]
The correct answer is D, -5 1/3.

The reason is that on a number line -3 1/4 would be placed to the right of -5 1/3.

The further you are to the right on the number line, the bigger the number.
4 0
3 years ago
The triangle below is isosceles. Find the length of side x in simplest radical form with
BigorU [14]
That all cause u the length of the time

6 0
2 years ago
Read 2 more answers
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8090 [49]

Answer:

Ok so I think the answer is 4.8 points per minute

Step-by-step explanation:

Why because Uncle Drew scored 28 points in 5 \frac{5}{6} minutes. We have to convert the mixed fraction first:

t = 5 \frac{5}{6}=\frac{5\cdot 6+5}{6}=\frac{35}{6}

So, the time is 35/6 minutes.

In order to find the number of points he scored in a minute, we have to divide the total number of points by the number of minutes, so:

mean = \frac{28}{35/6}=28 \cdot \frac{6}{35}=4.8

So, he scored 4.8 points per minute.

I hope you foundthis helpful.

3 0
2 years ago
Read 2 more answers
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