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2 years ago

Find the inverse of each function.

Mathematics

1 answer:

Novosadov [1.4K]2 years ago

3 0

as you should know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables and then solve for "y".

$\stackrel{f(x)}{y}=\sqrt{x}-5\implies \stackrel{\textit{quick switcheroo}}{x=\sqrt{y}-5}\implies x+5=\sqrt{y} \implies (x+5)^2=y \\\\\\ \stackrel{F~O~I~L}{(x+5)(x+5)}=y\implies x^2+10x+25=\stackrel{f^{-1}(x)}{y}$

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The price of an iPod dropped from $299.99 to $180.55. What was the percent decrease in price? (Round to nearest hundredth percen

anzhelika [568]

The price dropped 299.99 - 180.55 = 119.44. So we need to find out what percentage 119.44 is of 299.99.

"119.44 is what percentage of 299.99" translates to 
119.44 = x * 299.99 

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3 years ago

Read 2 more answers

Let f be a continuous function on the closed interval [ − 2 , 5 ]. If f((-2)=-7 and f(5)=1, then the Intermediate Value Theorem

azamat

Answer:

The function has at least 1 zero within the interval [-2,5].

Step-by-step explanation:

The intermediate value theorem states that, for a function continuous in a certain interval $[a,b]$ , then the function takes any value between $f(a)$ and $f(b)$ at some point within that interval.

This theorem has an important consequence:

If a function $f(x)$ is continuous in an interval [a,b], and the sign of the function changes at the extreme points of the interval:

$f(a)>0\\f(b)$ (or viceversa)

Then the function f(x) has at least one zero within the interval [a,b].

We can apply the theorem to this case. In fact, here we have a function f(x) continuous within the interval

[-2,5]

And we also know that the function changes sign at the extreme points of the interval:

$f(-2)=-70$

Therefore, the function has at least 1 zero within the interval [-2,5], so there is at least one point x' within this interval such that

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6 0

3 years ago

2.6 as a repeating decimal into a simplified fraction

sveticcg [70]

2 2/3

Put them together it’s a mixed fraction

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3 years ago

The ratio of Aziz's money to Osman's money was 2:1 at first. After Aziz spent $10 ratio became 4:3. How much money did each boy

Dvinal [7]

Answer:

Aziz's money was $30

Osman's money was $15

Step-by-step explanation:

Let

x-----> Aziz's money at first

y-----> Osman's money

we know that

$\frac{x}{y}=\frac{2}{1}$

$x=2y$ ------> equation A

$\frac{x-10}{y}=\frac{4}{3}$ -----> equation B

substitute equation A in equation B and solve for y

$\frac{2y-10}{y}=\frac{4}{3}\\ \\6y-30=4y\\ \\6y-4y=30\\ \\2y=30\\ \\ y=15$

Find the value of x

$x=2(15)=30$

therefore

At first

Aziz's money was $30

Osman's money was $15

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2 years ago

What is the answer to (8y -6

scZoUnD [109]

Answer:

Step-by-step explanation:

Incomplete presentation of question. Did you want to factor out the greatest common factor (which is 2), obtaining 2(4y - 3)? Or something else? Also: please note that if you use the left parenthesis ) , you MUST also use the right parenthesis ( .

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2 years ago