The slope of the line below is-2. Which of the following is the point-slope form of the line?

Determine whether each function has an inverse function. If it does, find the inverse function and state any restrictions on its

Talja [164]

QUESTION 1

The given function is;

$f(x) = |x - 6|$

This is an absolute value function.

For this function to have an inverse it must be a one-to-one function.

This absolute value function is not one-to-one
because

$f( 5)=1$
and

$f(7) = 1$

Since this function has more than one x-value mapping onto one y-value, it is not one-to-one and cannot have an inverse.

You can see from the graph that this function cannot pass the horizontal line test.

QUESTION 2

The given function is

$f(x) = \sqrt{6 - {x}^{2} }$

Let

$y= \sqrt{6 - {x}^{2} }$

This implies that,

${y}^{2} + {x}^{2} = 6$

We see clearly that, this function is a circle that is centered at the origin.

This means that,

$f(x) = \sqrt{6 - {x}^{2} }$

is a semicircle.

This function will not pass the horizontal line test and hence does not have an inverse.

QUESTION 3

The given function is

$h(x) = \frac{x+4}{3x-5}$

If we put

$h(a) = h(b)$

We obtain,

$\frac{a+4}{3a-5} = \frac{b+4}{3b-5}$

$(a + 4)(3b - 5) = (b + 4)(3a - 5)$

$3ab - 5a + 12b - 20 = 3ab - 5b + 12a - 20$

$- 17a = - 17b$

$a = b$

This shows that h(x) has an inverse because it is one-to-one.

Let

$y=\frac{x+4}{3x-5}$

We interchange x and y to get,

$x=\frac{y+4}{3y-5}$

$x(3y - 5) = y + 4$

$3xy - 5x = y + 4$

Group like terms to get,

$3xy - y = 5x + 4$

Factor to get,

$y(3x - 1) = 5x + 4$
Solve for y,

$y = \frac{5x + 4}{3x - 1}$

Hence

${f}^{ - 1}(x) = \frac{5x + 4}{3x - 1}$

where

$x \ne \frac{1}{3}$

6 0

3 years ago

The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the probability that there will

Makovka662 [10]

Answer:

(a) more than 2 such accidents in the next month $\approx 0.3773$

(b) more than 4 such accidents in the next 2 months $\approx 0.44882$

(c) more than 5 such accidents in the next 3 more than 5 such accidents in the next 3 months $\approx 0.64533$

Step-by-step explanation:

Let N be the Random variable that marks the number of crashes in certain month.

Now let us use Poisson distribution since we are given with average number of crashes that is N \sim Pois(2.2)

(A) more than 2 such accidents in the next month

Probability(more than 2 such accidents in the next month)=P(N>2)

P(N>2)=1-P(N=0)-P(N=1)-P(N=2)

=> $1-e^-{2.2}-2.2e^{-2.2}-\frac{2.2^2}{2!}e^{2.2}$

=> $\approx 0.3773$

B) more than 4 such accidents in the next 2 months

since the average number of crashes in 1 month is 2.2, the average number of crashes in two months is 4.4. hence, if we say that $N_1$ is the number of crashes in 2 months, we have that $N\sim$ Pois(4.4)

Thus,

Probability(more than 4 such accidents in the next 2 months)=P( $N_1>4$ )

= $1-P(N_1=0)-P(N_1=1)-P(N_1=2)=P(N_1=3)-P(N_1=4)$

$1-\sum_{k=1}^{4} \frac{4.4^{k}}{k !} e^{-4.4}$

=> $\approx 0.44882$

C) more than 5 such accidents in the next 3 more than 5 such accidents in the next 3 months

If we say that $N_2$ marks the number of crashes in the next 3 months , using the same argument as in (a) we have that a $N\sim$ Pois(6.6)

Hence

P( $N_2>5$ )= $1-\sum_{k=0}^{5} \frac{6.6^{k}}{k !} e^{-6.6}$

=> $\approx 0.64533$

6 0

4 years ago

What’s the correct answer for this question?

sp2606 [1]

A total of 13 teens were surveyed.

8 of those read books.

The probability would be 8/13 = 0.6153

Rounded to the nearest hundredth = 0.62

8 0

4 years ago

Which of the following is the equation of the line?

muminat

Answer:

C. y = 2/3x - 2

Step-by-step explanation:

we already have both the y-intercept (b) and the slope (m)

so all we have to do is put it in the slope-intercept form or y=mx+b

y = 2/3x - 2

4 0

3 years ago

The graph of function f is shown. Function g is represented by the equation. Look at the graph and picture!

lana66690 [7]

Answer: B) different y intercepts; same end behavior

=======================================================

Explanation:

The graph shows the y intercept is 4 as this is where the green curve crosses the vertical y axis.

The y intercept of g(x) is 6 which can be found by plugging x = 0 into the g(x) function

g(x) = 4(1/4)^x + 2

g(0) = 4(1/4)^0 + 2

g(0) = 6

So we can see the y intercepts are different.

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However, the end behaviors are the same for each function. The left side of f(x) goes up forever to positive infinity. The same is true for g(x). You could use a graphing calculator or a table to see this. As x heads to negative infinity, y goes to positive infinity.

In terms of symbols, $x \to -\infty, y \to \infty$

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For the right side of f(x), it slowly approaches the horizontal asymptote y = 2. It never actually reaches this y value. The same happens with g(x). The portion 4(1/4)^x gets smaller but never gets to 0 so overall 4(1/4)^x+2 gets closer to 2. We can say that as x approaches infinity, y approaches 2.

In terms of symbols, $x \to \infty, y \to 2$

6 0

4 years ago