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Alekssandra [29.7K]
2 years ago
13

Let f ( ) sin(arctan ) x x = . What is the range of f ?

Mathematics
1 answer:
nikklg [1K]2 years ago
5 0
<span>So you have composed two functions,
</span><span>h(x)=sin(x) and g(x)=arctan(x)</span>
<span>→f=h∘g</span><span>
meaning
</span><span>f(x)=h(g(x))</span>
<span>g:R→<span>[<span>−1;1</span>]</span></span>
<span>h:R→[−<span>π2</span>;<span>π2</span>]</span><span>
And since
</span><span>[−1;1]∈R→f is defined ∀x∈R</span><span>

And since arctan(x) is strictly increasing and continuous in [-1;1] ,
</span><span>h(g(]−∞;∞[))=h([−1;1])=[arctan(−1);arctan(1)]</span><span>
Meaning
</span><span>f:R→[arctan(−1);arctan(1)]=[−<span>π4</span>;<span>π4</span>]</span><span>
so there's your domain</span>
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irina [24]

Answer:

<u>Laura has to walk at 2 1/4 miles per hour or faster to arrive to her job on time.</u>

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Distance from Laura's home to her job = 4 1/2 miles

Time when Laura starts to walk to her job : 9:00 a.m.

Time when Laura is scheduled to start working : 11:00 a.m.

2.  Will she arrive at her job on time?

Time Laura has to complete the distance from her home to her job = 2 hours (11 -9)

Speed that Laura need to walk to arrive to her job on time = Distance from Laura's home to her job/Time Laura has to complete the distance from her home to her job

Speed that Laura need to walk to arrive to her job on time = 4 1/2 miles/2 hours = (4 1/2)/2 = (9/2)/2 = 9/2 * 1/2 = 9/4 = 2 1/4

Speed that Laura need to walk to arrive to her job on time = 2 1/4 miles per hour.

<u>Laura has to walk at 2 1/4 miles per hour or faster to arrive to her job on time.</u>

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2 years ago
Determine whether the system of linear equations has one solution infinitely many solutions or no solution explain your reasonin
hammer [34]

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Step-by-step explanation:

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y = 3x- 5

3x + 5 = 3x -5

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Answer:

The equation is following the mathematical rule of multiplying exponents.

Step-by-step explanation:

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Hope this helps explain multiplying exponents together, and the mathematical rule behind it.

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