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sdas [7]
3 years ago
6

Find the values of x for which the combined function h(x) =f(x)/g(x) is undefined if f(x) = 5x + 1 and g(x) = x2 - 9.

Mathematics
2 answers:
bulgar [2K]3 years ago
8 0

Answer:

For x = 3 or x = -3 h(x) =f(x)/g(x) is undefined.

Step-by-step explanation:

Given  : h(x) =f(x)/g(x) is undefined if f(x) = 5x + 1 and g(x) = x² - 9.

TO find : Find the values of x for which the combined function h(x) =f(x)/g(x) is undefined .

Solution : We have given that

f(x) = 5x + 1 and g(x) = x² - 9.

Function is undefined when denominator  of fraction is zero .

In h(x) =f(x)/g(x)

Here , g(x)  is the denominator then g(x) =0

x² - 9 = 0

On adding by 9 both sides

x² - 9 + 9 = +9.

x² = 9

Taking square root both sides

x = \sqrt{9}

x = ± 3

x = 3 , x = -3

Therefore, For x = 3 or x = -3 h(x) =f(x)/g(x) is undefined.

neonofarm [45]3 years ago
3 0
Hello : 
<span>the function h(x) =f(x)/g(x) is undefined : x²-9 =0
(x-3)(x+3)=0
x-3=0 or x+3=0
</span><span> the values  : </span>x=3 or x= -3
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A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square val
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Answer:

\chi^2_{\alpha/2}=43.195

\chi^2_{1- \alpha/2}=14.573

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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The confidence interval for the population variance is given by the following formula:

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We need on this case to calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=28-1=27

Since the Confidence is 0.95 or 95%, the value of \alpha=1-0.95=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table for the Chis square distribution with 27 degrees of freedom to find the critical values. We need a value that accumulates 0.025 of the area on the left tail and 0.025 of the area on the right tail.  

The excel commands would be: "=CHISQ.INV(0.025,27)" "=CHISQ.INV(0.975,27)". so for this case the critical values are:

\chi^2_{\alpha/2}=43.195

\chi^2_{1- \alpha/2}=14.573

b. 14.573 and 43.195.

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