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LuckyWell [14K]
3 years ago
12

Given that f(x) =

Mathematics
1 answer:
bija089 [108]3 years ago
4 0

Answer:

f(x)=\sqrt[3]{x} +5\\\\\implies y = \sqrt{3}{x}+5

a) Since the function is given to be one - one so the inverse of the function exist. Now f(x) maps x to y so the inverse of f(x) maps y to x

To find inverse, first interchange the roles of x and y :

\implies x = \sqrt[3]{y}+5

Now, solve for y :

x = \sqrt[3]{y}+5\\\\\implies \sqrt[3]{y}=x-5\\\\\text{Now, cubing both the sides. We get,}\\\\\implies y=(x-5)^3\\\\\implies y=x^3-15\cdot x^2+75\cdot x-125\\\\\implies\bf f^{-1}(x)=x^3-15\cdot x^2+75\cdot x-125

b) To find coordinates of f(x) :

f(x)=\sqrt[3]{x} +5

First take y = 0 then take x = 0

⇒ x-coordinates : (-125,0) and y-coordinates : (0,5)

To find coordinates of inverse function of x :

y=x^3-15\cdot x^2+75\cdot x-125

First take y = 0 then take x = 0

⇒ x - coordinates : (5,0) and y - coordinates : (0,-125)

c)  f(x) is defined for every real number.

⇒ Domain : -∞ < x < ∞

and Range : -∞ < f(x) < ∞

And inverse function of x is also defined for every real number :

⇒ Domain : -∞ < x < ∞

\text{and Range : }-\infty < f^{-1}(x) < \infty

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Answer:

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Step-by-step explanation:

The distance formula states that the distance between two points (a,b) and (c,d) is \sqrt{(a-c)^2+(b-d)^2}.

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Simplifying with order of operations, first using the distributive property, gives

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Squaring and adding gives

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A recent survey indicated that the average amount spent for breakfast by business managers was $9.33 with a standard deviation o
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Answer:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

Replacing the info given we got:

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Step-by-step explanation:

Information given

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\mu_o =9.33 represent the value to verify

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Hypothesis to test

We want to test if the true mean is higher than 9.33, the system of hypothesis would be:  

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Alternative hypothesis:\mu > 9.33  

The statistic is given by:

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Replacing the info given we got:

t=\frac{9.41-9.33}{\frac{0.24}{\sqrt{81}}}=3    

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