What is the range of the function y=3√x+8? -∞xy<∞ -8 0≤y<∞ 2≤y<∞

Mathematics

1 answer:

sdas [7]2 years ago

6 0

The range of the function the as given in the equation is; -∞ ≤ y < ∞.

<h3>What is the range of the function?</h3>

It follows from the task content that the function given is; y=3√x+8.

On this note, it follows that the range of the function is the set of all possible outputs, y values and in this case is; -∞ ≤ y < ∞.

It therefore follows that the range of the function is as indicated above as all X-values (domain) must be positive and the square root of x yields a positive or negative real number.

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For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

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Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

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so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so: