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3 years ago

Domain and range of f(x)=sqrt(x^2 -4)

Mathematics

1 answer:

antoniya [11.8K]3 years ago

3 0

Answer:

See explanation

Step-by-step explanation:

The domain of this function is all real numbers, since no matter what x value you input you will get a y value. The range of this function is $(-4,\infty)$ , because no matter what x value you input, you cannot go below -4. Hope this helps!

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What is the solution of the system? Use the elimination method.

Yuki888 [10]

I got D.There is no solution

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3 years ago

Simplify: 2⁶X5⁴X3¹²/2²x5²x3⁴

Sholpan [36]

Step-by-step explanation:

2⁶X5⁴X3¹²/2²x5²x3⁴

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2 years ago

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Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

3 years ago

Layla has 5.49 pounds of wood she divides it into 7 <br> so basically 5.49÷7

Nuetrik [128]

Answer:

0.7842857142857143

Step-by-step explanation: i would right an explanation but i cant put it all so you will just have to trust me

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2 years ago

A system of equations is shown below. Which of the following statements describes the graph of this system of equations in the (

ollegr [7]

The given system of equations represent a single line with positive slope. So option C is correct.

<u>SOLUTION: </u>

Given system of equations are

$\begin{array}{l}{3 y-5 x=15 \rightarrow(1)} \\\\ {6 y-10 x=30 \rightarrow(2)}\end{array}$

Now, if we observe, $(1) \times 2 \rightarrow(2)$ multiplying the $1^{st}$ equation with 2 results in $2^{nd}$ equation.

which means the two line equations represents the same line.

Now, let us find the slope of line, $\text { slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-3}{-5}=\frac{3}{5}=\text { positive slope }$

So, the line has a positive slope.

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3 years ago