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<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>
J=amount Jake has; F=amount Fred has=2J
J+F=$54
J+2J=$54
3J=$54
J=$18
ANSWER 1: Jake has $18.
F=2J=2($18)=$36 ANSWER 2: Fred has $36.
Answer: The first one is 2 2/3 and the second one is 10 1/2
Step-by-step explanation: So 2/3 divided by 1/4. First you would do keep, change, flip. Then that would give you 2/3 times 4/1. 2/3 times 4/1 would be 8/3 which can be simplified to 2 2/3. The second one 7 divided by 2/3. Again do keep, change, flip. 7 times 3/2. This would give you 21/2 when you simplify you get 10 1/2.
