Answer:
B. x = 2
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
check by substituting each given value of x into the function
x = 0 ⇒ y = × 0² = 0
hence (0, 0) is correct
x = 2 ⇒ y = × 4 = 3
hence (2, 4 ) is incorrect
x = 3 ⇒ y = × 9 = 6
hence (3, 6 ) is correct
x = 5 ⇒ y = × 25 = 18
hence (5, 18 ) is correct
<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>
As A Simplified Fraction She Only Has 1/4 Of Her Allowance Left
(cos(x) + cos(y))^2 + (sin(x) - sin(y))^2 Remove the brackets
cos^2(x) + cos^2(y) + 2cos(x)*cos(y) + sin^2(x) - 2(sin(x)*sin(y) + sin^2(y) Combine these two in bold to make 1 because sin^2(x) + cos^2(x) = 1
1 + cos^2(y) + 2cos(x)*cos(y) - 2*sin(x)*cos(y) + sin^2(y)
These two in bold also make 1
2 + 2cos(x)*cos(y) - 2*sin(X)*sin(y) Bring out a common factor of 2
2 +2(cos(x)*cos(y) - sin(x)*sin(y) )
but cos(x+y ) = cos(x)*cos(y) - sin(x)*sin(y)
2 + 2* cos(x + y) is your final answer.
