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marishachu [46]
3 years ago
13

The inverse of the function g(x)=x−65 can be written in the form g−1(x)=ax+b. What is the value of a?

Mathematics
1 answer:
Anna35 [415]3 years ago
3 0

9514 1404 393

Answer:

  a = 1

Step-by-step explanation:

The slope of the inverse of a linear function is the inverse of the slope of the original function.

The slope of g(x) is the coefficient of x: 1.

The inverse of 1 is 1/1 = 1.

The slope of the function g^-1(x) is 1, so a=1.

_____

<em>Additional comment</em>

  g^-1(x) = x +65 . . . . . a=1; b=65

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The confidence interval for the difference of two proportions would be given by this formula  

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For this case we have the confidence interval given by: (-0.0313,0.2753). From this we can find the margin of erro on this way:

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ME=z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}

We have all the values except the value for z_{\alpha/2}

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0.1533=z_{\alpha/2} \sqrt{\frac{0.768(1-0.768)}{92} +\frac{0.646 (1-0.646)}{95}}

And solving for z_{\alpha/2} we got:

z_{\alpha/2}=2.326

And we can find the value for \alpha/2 with the following excel code:

"=1-NORM.DIST(2.326,0,1,TRUE)"

And we got \alpha/2 =0.01 so then the value for \alpha=0.02 and then the confidence level is given by: Conf=1-0.02=0.98 or 98%

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