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Chapter 2: Problem 61

Find the domain of the expression. Use a graphing utility to verify your result. $$\sqrt{4-x^{2}}$$

Short Answer

Expert verified
The domain of the expression \(\sqrt{4 - x^{2}}\) is \(-2 \leq x \leq 2\).

Step by step solution

01

Understanding the expression

For the expression \(\sqrt{4-x^{2}}\), we need to find all values of x for which the expression has a real value.
02

Solving the inequality

The expression inside the square root must be greater than or equal to zero. Therefore we can start off by setting up the inequality: \(4 - x^{2} \geq 0\)
03

Find the values of x

From the inequality \(4-x^{2} \geq 0\), we can positive or zero values of x. To do this, first rearrange the inequality to the form: \(x^{2} \leq 4\). Taking the square root of both sides: \(|x| \leq 2\). This gives us the range of x: \(-2 \leq x \leq 2\)
04

Final Result

Therefore the domain of the expression is \(-2 \leq x \leq 2\)

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Most popular questions from this chapter

Find the rational zeros of the polynomial function. $$f(x)=x^{3}-\frac{3}{2} x^{2}-\frac{23}{2} x+6=\frac{1}{2}\left(2 x^{3}-3 x^{2}-23 x+12\right)$$

Write the polynomial as the product of linear factors and list all the zeros of the function. $$g(x)=x^{3}-3 x^{2}+x+5$$

Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{2}-x+56$$

The coordinate system shown below is called the complex plane. In the complex plane, the point that corresponds to the complex number \(a+b i\) is \((a, b)\) (GRAPH CANNOT COPY) Match each complex number with its corresponding point. (i) 3 (ii) \(3 i\) (iii) \(4+2 i\) (iv) \(2-2 i\) (v) \(-3+3 i\) (vi) \(-1-4 i\)

Find all the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to disregard any of the possible rational zeros that are obviously not zeros of the function. $$f(s)=2 s^{3}-5 s^{2}+12 s-5$$
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