All categories

3 years ago

Find the domain of the function

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

7 0

Answer:

The domain of f is (-∞,4)

Step-by-step explanation:

Domain of a Function

The domain of a function f is the set of all the values that the input variable can take so the function exists.

We are given the function

$f(x)=\frac{1}{\sqrt{4-x} }$

It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:

4 - x > 0

Subtracting 4:

- x > -4

Multiplying by -1 and swapping the inequality sign:

x < 4

Thus the domain of f is (-∞,4)

You might be interested in

According to a study, an average of six cell phone thefts is reported in San Francisco per day. Assume that the number of report

lions [1.4K]

Answer:0.29

Step-by-step explanation:

An average of six cell phone thefts is reported in San Francisco per day. This means our mean value, u = 6

For poisson distribution,

P(x=r) = (e^-u×u^r)/r!

probability that four cell phones will be reported stolen tomorrow=

P(x=4)= (e^-6×6^4)/4!

= (0.00248×1296)/4×3×2×1

= 3.21408/24=

0.13392

P(x=5)= (e^-6×6^5)/5!

= (0.00248×7776)/5×4×3×2×1

= 19.28448/120

= 0.1607

probability that four or five cell phones will be reported stolen tomorrow

= P(x=4) + P(x=5)

= 0.13392 + 0.1607

= 0.294624

Approximately 0.29

8 0

3 years ago

According to the key of a particular park map, every 8 inches on the map represents 3 miles of trails in the park. How many inch

MA_775_DIABLO [31]

Answer:

24 inches represents 9 miles in the map

Step-by-step explanation:

To solve this problem you take into account that 8 inches represents 3 miles and that x represent the number of inches for 9 miles. That is:

8 ------- 3

x ------- 9

This is simply a rule of three, then you calculate:

$x=\frac{8\ x\ 9}{3}=\frac{72}{3}=24$

Hence, 24 inches represents 9 miles in the map

8 0

3 years ago

Douglas is placing strings of lights around the edge of a circular patio with a diameter of 7.5 meters. The lights are in length

OLEGan [10]

17 is the correct answer hope this helps, and have a nice day

4 0

3 years ago

Read 2 more answers

If George the giraffe is 18 feet tall how many inches tall is he

vitfil [10]

The answer is 216 inches

3 0

3 years ago

When a certain number is divided by 24,36 or 50 the remainder is 3 in each case.find the number

Lady bird [3.3K]

Answer:

$\color{orange}{1803}$

Step-by-step explanation:

Let the number be 'x'

Using the general formula

Divided number = (Quotient × Dividend) + Remainder

Where Quotient is an integer

When divided by 24..

x = 24P + 3

Where P is an integer

When divided by 36..

x = 30Q + 3

Where Q is an integer

When divided by 50..

x = 50R + 3

Where R is an integer

Therefore..

24P = 36Q = 50R

L.C.M of their co-oficients is 1800

$1800 \frac{P}{75} =1800 \frac{Q}{50} =1800 \frac{R}{36}$

$\frac{P}{75}=\frac{Q}{50} =\frac {R}{36}$

For smallest values for integers P, Q and R

P = 75, Q= 50 and R = 36

Substitute any of the values to find x

x = 24P + 3

x = 24(75) + 3

x = 1800 + 3

x = 1803

Hope it helps

4 0

3 years ago