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Zina [86]
4 years ago
12

If g(x) = 3x + 2 and h(x) = 9x2 + 12x + 6, find a function f such that f ○ g = h

Mathematics
1 answer:
Virty [35]4 years ago
6 0
F(g(x)) = f(3x+2) = h(x)=9x^2+12x + 6

Note that (3x+2)^2 = 9x^2 + 12x + 4, which is almost, but not quite, equal to h(x).

Let's experiment.  What if f(x) = x^2 + 2?

Then f(3x+2) = (3x+2)^2 + 2 = 9x^2 + 12x + 4 + 2 = 9x^2 + 12x + 6, which is the same as the given h(x).

Thus, f(x) is x^2 + 2.
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Write ln(x^3y^2) in terms of u and v (picture provided)
Katena32 [7]

Remember the properties of logarithms. If you have ln81, you can pull out the power of two (9^2) and have 2ln9. Also, you could do ln9 + ln9 because 9*9=81 and ln9*9 = ln9 + ln9

With these properties, you can get 3lnx+2lny, which is 3u+2v according to the answer.

Hope I helped!

6 0
3 years ago
Find the roots of the equation x^2+2x+5=0
stiv31 [10]

Answer:

x = - 1 ± 2i

Step-by-step explanation:

we can use the discriminant b² - 4ac to determine the nature of the roots

• If b² - 4ac > , roots are real and distinct

• If b² - 4ac = 0, roots are real and equal

• If b² - ac < 0, roots are not real

for x² + 2x + 5 = 0

with a = 1, b = 2 and c = 5, then

b² - 4ac = 2² - (4 × 1 × 5 ) = 4 - 20 = - 16

since b² - 4ac < 0 there are 2 complex roots

using the quadratic formula to calculate the roots

x = ( - 2 ± \sqrt{-16} ) / 2

  = (- 2 ± 4i ) / 2 = - 1 ± 2i


7 0
4 years ago
A bag contains colored tiles.
Iteru [2.4K]

Answer:

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Step-by-step explanation:

add up the amount of tiles

6+3+3=12

then subtract the green tiles from the total amount

12-6=6

then divide 12/6

=0.5

3 0
3 years ago
Read 2 more answers
How many terms does this expression have: 4 + 6c - 14 + 1 *
Alika [10]

Answer:

4

Step-by-step explanation:

4 is one term, 6c is one term, 14 is one term, and 1 is a term. total=4.

6 0
3 years ago
How do you change y=x^2-10x-6 into vertex form
In-s [12.5K]

Converting to vertex form is actually pretty simple so I think you might find something to help you out here. :)

https://mathbitsnotebook.com/Algebra1/Quadratics/QDVertexForm.html

3 0
3 years ago
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