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4 years ago

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Find the domain and range for the following functions:

1 answer:

Andreyy894 years ago

4 0

Answer with Step-by-step explanation:

Since we have given that

a. f: ℝ → ℝ given by f(x) = x + 2

Domain would be all real numbers i.e. (-∞, ∞)

Range would be all real numbers i.e. (-∞, ∞)

b. g: ℝ → ℝ given by g(x) = √x − 1

Domain would be all positive numbers i.e. [0,∞)

Range would be [-1,∞)

c. f(g(x))

$f(g(x))=f(\sqrt{x}+1)=\sqrt{x}+1+2=\sqrt{x}+3$

Domain would be [0,∞)

Range would be [3,∞)

d. g(f(x))

$g(x+2)=\sqrt{x+2}-1$

Domain would be [-2,∞)

Range would be (0,∞)

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Tems11 [23]

QUESTION A

The given multiplication problem is

$\frac{39}{64} \times \frac{8}{13}$

Factor each term to obtain;

$\frac{13\times 3}{8\times8} \times \frac{8}{13}$

Cancel out the common factors to obtain;

$\frac{1\times 3}{8\times1} \times \frac{1}{1}$

Simplify to get;

$\frac{3}{8}$

QUESTION B

The given multiplication problem is

$\frac{2}{3}\times \frac{1}{5}\times \frac{4}{7}$

This the same as

$\frac{2\times 1\times 4}{3\times 5\times 7}$

This simplifies to;

$\frac{8}{105}$

QUESTION C

The given problem is

$\frac{3}{5}\times \frac{10}{12} \times \frac{1}{2}$

This is the same as

$\frac{3}{5}\times \frac{5}{6} \times \frac{1}{2}$

$=\frac{1}{1}\times \frac{1}{2} \times \frac{1}{2}$

This simplifies to

$=\frac{1}{4}$

QUESTION D.

The given expression is

$\frac{4}{9}\times 54$

Factor the 54 to obtain;

$\frac{4}{9}\times 9\times 6$

Cancel the common factors to get;

$\frac{4}{1}\times 1\times 6$

This simplifies to;

$=24$

QUESTION E

The given problem is

$20\times 3\frac{1}{5}$

Convert the mixed numbers to improper fraction to obtain;

$=20\times \frac{16}{5}$

$=4\times5 \times \frac{16}{5}$

Cancel the common factors to get;

$=4\times1 \times \frac{16}{1}$

$=64$

QUESTION F

The multiplication problem is

$11 \times 2 \frac{7}{11}$

Convert the mixed numbers to improper fractions to obtain;

$11 \times \frac{29}{11}$

Cancel out the common factors to get;

$=1 \times \frac{29}{1}$

Simplify;

$=29$

QUESTION G

The given problem is

$5\frac{1}{3}\times 5\frac{1}{8}$

Convert to improper fractions;

$=\frac{16}{3}\times \frac{41}{8}$

Cancel out the common factors to get;

$=\frac{2}{3}\times \frac{41}{1}$

$=\frac{82}{3}$

Convert back to mixed numbers

$=27\frac{1}{3}$

QUESTION H

The given expression is

$10\frac{2}{3} \times 1\frac{3}{8}$

Convert to improper fraction to get;

$\frac{32}{3} \times \frac{11}{8}$

Cancel common factors to get;

$=\frac{4}{3} \times \frac{11}{1}$

Simplify

$=\frac{44}{3}$

Convert back to mixed numbers;

$=14\frac{2}{3}$

7 0

3 years ago

A group of 2n people, consisting of n men and n women, are to be independently distributed among m rooms. Each woman chooses roo

vfiekz [6]

Step-by-step explanation:

Assume that

$X_i = \left \{ {{1, If , Ith, room, has,exactly, 1,man, and , 1,woman } \atop {0, othewise} \right.$

hence,

$x = x_1 + x_2+....+x_m$

now,

$E(x) = E(x_1+x_2+---+x_m)\\\\E(x)=E(x_1)+E(x_2)+---+E(x_m)$

attached below is the complete solution

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3 years ago

Please thank you so much yall

Leto [7]

19. There are 24 hours in a day and Maria travelled for 15 days so multiply the two:
24*15=360

So Maria travelled for 360 hours.

22a. False; 2,000 lbs = 1 Ton
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3 years ago

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Particles of dust from meteors can travel at speeds up to 30 miles per second. How many miles is that per minute?

ikadub [295]

Answer: 1,800 miles per minute

Step-by-step explanation: 30 * 60= 1,800

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What is 4/3 divided by 5/2

Anna [14]

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