<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>
The answer would be -4 because when you add a positive and a negative it’s like subtracting.
The equation that can be used to model the situation regarding the e-books and paperback is 5x + 12y = 68
The following information can be gotten from the question:
Total amount spent on e-books and paperback = $68
<em>Cost</em><em> of e-book = $5 each.</em>
<em>Cost of paperback = $12 each</em>
<em>Number of</em><em> e-books</em><em> = x</em>
<em>Number of paperbacks = y</em>
Therefore, the equation that can be used to model the situation regarding the <em>e-books </em>and <em>paperback</em> will be:
= 5(x) + 12(y) = 68
5x + 12y = 68
The equation will be 5x + 12y = 68
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For this case we have the following functions:
We must find 
. By definition we have to:
So:
Finally, the composite function is:
Answer:
