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Mila [183]
3 years ago
8

The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
3 0
Solve for k for each value of the range, and you will obtain each value of k that may belong to the domain

1) k^2 +2k +1 = 25

k^2 + 2k -24 = 0

(k + 6)(k- 4) = 0
k + 6 = 0 ⇒ k = - 6

k - 4 = 0 ⇒ k = 4

2) k^2 + 2k + 1 = 64

k^2 + 2k - 63 = 0

(k +  9)(k -  7) = 0

k + 9 = 0 ⇒ k = -9
k - 7 = 0 ⇒ k = 7

Then the largest possible domain is {-9, -6, 4, 7}

You might exclude one from -6 and 4 but not both.

You might also exclude one from -9 and 7 but not both

Because with those sets you will obtain all the images that are in the range.

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Answer:

Step-by-step explanation:

Based on the two graphs I see at the bottom of the photo, you're looking at a quadratic function. The answer you put in is a linear equation.

Quadratic functions follow the form ax^2+bx+c, where a, b, and c can be either positive or negative constants.

The table says that the equation, when graphed, should start at the top, slide to the bottom, and then slide back up to the top. So a must be positive.

c has to be -8 since it's the y-intercept.

So far, our equation is ax^2+bx-8. We'll need to plug in some points in order to work out what a and b are.

Let's use (-2,5) as the first set of points, and (4,14) as the second set.

5=a(-2)^2+b(-2)-8\\14=a(4)^2+b(4)-8\\

Now we have 2 equations with 2 unknowns. Solve for one variable:

5=4a-2b-8\\13+2b=4a\\\frac{13+2b}{4}=a

Now substitute that into the second equation:

14=(\frac{13+2b}{4})(4^2)+4b-8\\14+8=(13+2b)(4)+4b\\22-52=8b+4b\\-30=12b\\-\frac{30}{12}=-\frac{10}{4}=-\frac{5}{2}=b

Now substitute the result into the first equation.

\frac{13+2(-\frac{5}{2})}{4}=a\\\\\frac{13-5}{4}=a\\\\\frac{8}{4}=a\\\\ 2=a

Now substitute our values back into the original equation:

y(x)=2x^2-\frac{5}{2}x-8

Please let me know if this is correct.

8 0
3 years ago
<img src="https://tex.z-dn.net/?f=9x%5E%7B2%7D" id="TexFormula1" title="9x^{2}" alt="9x^{2}" align="absmiddle" class="latex-form
sweet-ann [11.9K]

Answer:

12x^2

Step-by-step explanation:

All you need to do is combine like terms

since 9x^2 and 3x^2 are like terms with the same variable and same degree, they can be combined to get 12x^2

3 0
2 years ago
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Your answer would be 1.00$ because if you subtract all that is given from the problem you get 10-9, which equals 1.
6 0
3 years ago
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Answer:

44.9%

Step-by-step explanation:

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