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WINSTONCH [101]
3 years ago
8

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

Mathematics
1 answer:
Effectus [21]3 years ago
7 0
<span>k^2 + 2k + 1 = 25
</span><span>k^2 + 2k + 1 - 25 = 0
</span><span>k^2 + 2k  - 24 = 0
(k - 4)(k + 6) = 0
k - 4 = 0; k = 4
k + 6 = 0; k = -6

</span>k^2 + 2k + 1 = 64
k^2 + 2k + 1 - 64 = 0
k^2 + 2k  - 63 = 0
(k - 7)(k + 9) = 0
k - 7 = 0; k = 7
k + 9 = 0; k = -9

x = -9, -6, 4, 7

answer
<span>D. {4, 7}</span>

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<u>Solution:</u>

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<em><u>We have to check option by option. </u></em>

Now, (-2, 1) ⇒ 1 – 4(-2) ≥ - 5 ⇒ 1 + 8 ≥ -5 ⇒ 9 ≥ -5 ⇒ correct answer.

Now, (-4, 2) ⇒ 2 – 4(-4) ≥ -5 ⇒ 2 + 16 ≥ - 5 ⇒ 18 ≥ - 5 ⇒ correct answer

Now, (1, -1) ⇒ -1 – 4(1) ≥ - 5 ⇒ -1 – 4 ≥ - 5 ⇒ -5 ≥ -5 ⇒ correct answer

Now, (4, 0) ⇒ 0 – 4(4) ≥ - 5 ⇒ -16 ≥ -5 ⇒ wrong answer

Now, (5, -2) ⇒ -2 – 4(5) ≥ - 5 ⇒ -2 – 20 ≥ -5 ⇒ -22 ≥ -5 ⇒ wrong answer

Hence, (-2, 1), (-4, 2) and (1, -1) are solutions to given inequality.

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Step-by-step explanatio

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Step-by-step explanation:

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