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2 years ago

Find the domain of the inverse of thefollowing functions

Mathematics

2 answers:

luda_lava [24]2 years ago

7 0

Answer:

f(x) = (3x - 7)/5

f^-1(x) = (5y + 7)/3

The DOMAIN is the set of all possible numbers that you can put in for the independent variable and get an answer. If you had g(x) = 1/x, you could NOT put in 0 for x and get an answer because 1/0 is undefined. So the domain is all numbers but 0.

The RANGE is the set of numbers you will get for the dependent variable. If you had g(x) = 1/x, you could NOT get 0 for g(x), no matter what you put in for x. So the range is all numbers but 0.

In both your functions the domain and the range equal all possible numbers. Or all real numbers.

Step-by-step explanation:

Another way to write the answers is:

D = {x | x = R} and R = {f(x) | f(x) = R} where

D = domain, R = range, { } means set, | is such that.

Marizza181 [45]2 years ago

7 0

Answer:

[-2, 4] or {-2, -1, 0, 1, 2, 3, 4}

Step-by-step explanation:

If you invert a func., it's range becomes the domain and it's domain becomes the range. So, if you want the domain of the inverted func, you'll need to find out the range of the original. That is, Domain of Inverse = Range of Original.

Range, pretty much, means the extremities bounds the y-values.

Here, for the original func., the y-extremities are -2 and +4, thus the range is [-2, 4] and hence the domain of the inverted func will be [-2, 4].

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3 years ago

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Select all the correct answers. Function g is a transformation of the parent exponential function. Which statements are true abo

lesantik [10]

The correct statements are:

Function g has a y-intercept of (0,4)

The range of the function g is (3, ∞).

The function g is positive over the interval (-∞ , ∞ ).

The parent function i.e. exponential function is defined by:

y=f(x)=aˣ

From the graph given below,

1. The graph of the function g is 3 units above the graph of the parent exponential function. as the parent exponential function aˣ cuts the y-axis at (0,1) and the child transformed function cut at (0,4) for which g is 4-1=3 units above the parent function

2. The domain of the function is set of all the inputs for which function is defined. From the graph of function g, it is clear tha the domain of the function is (-∞ , ∞ ) as the domain of the parent exponential function is also (-∞ , ∞ ).

3. The y-intercept is the point at which function cut the y-axis. Graph of function g cut the y-axis at (0, 4). Therefore, Function g has the y-intercept at (0,4).

4. From the graph it is clear that Function g increases over the interval (-∞, 0) .

5. The range of the function is the output values of the function. From the graph, it is observed that the range of function g is (3, ∞). as its minimum value is 3 then the maximum value is ∞.

6. As, the graph of function g is drawn above the x-axis. Therefore, Function g lies completely on +ve y-axis, so function g is positive over the interval (-∞ , ∞ ).

Therefore The correct statements are:

Function g has a y-intercept of (0,4)

The range of the function g is (3, ∞).

The function g is positive over the interval (-∞ , ∞ ).

Learn more about the exponential function

here: brainly.com/question/2456547

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2 years ago

The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What

Nutka1998 [239]

Answer:

The probability that an 18-year-old man selected at random is greater than 65 inches tall is 0.8413.

Step-by-step explanation:

We are given that the heights of 18-year-old men are approximately normally distributed with mean 68 inches and a standard deviation of 3 inches.

Let X = heights of 18-year-old men.

So, X ~ Normal( $\mu=68,\sigma^{2} =3^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean height = 68 inches

$\sigma$ = standard deviation = 3 inches

Now, the probability that an 18-year-old man selected at random is greater than 65 inches tall is given by = P(X > 65 inches)

P(X > 65 inches) = P( $\frac{X-\mu}{\sigma}$ > $\frac{65-68}{3}$ ) = P(Z > -1) = P(Z < 1)

= 0.8413

The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.

6 0

3 years ago

At age 16, Estelle weighed 110lbs.

Cloud [144]

Answer:

Her weight is increase by 18 lbs over past five years and the slope is 3.6 lbs per year.

Step-by-step explanation:

Given information: Estelle weight is

At age 16 = 110 lbs

At age 21 = 128 ibs

Increase in her weight over the past 5 years is the difference of weight at age 21 and at age 16.

Increase in her weight over the past 5 years = 128 - 110 = 18

Her weight is increase by 18 lbs over past five years.

Let x=age and y=weight, then the weight function passes through the points (16,110) and (21,128).

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ , then the slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}$

Using the above formula we get

$m=\frac{128-110}{21-16}$

$m=\frac{18}{5}$

$m=3.6$

Therefore the slope is 3.6 lbs per year.

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3 years ago

Show work please :)

fgiga [73]

Answer:

Step-by-step explanation:

90/100 = 54

Cross multiplying:

100 * 54 / 90

5400/90

4 0

2 years ago

Find the domain of the inverse of thefollowing functions​

Find the domain of the inverse of thefollowing functions