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masya89 [10]
2 years ago
5

Directions: Find the domain and range of each function

Mathematics
1 answer:
rjkz [21]2 years ago
5 0
Domain (-infinity,infinity)
Range (-infinity, infinity)
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Consider the functions f and g defined by \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt
tino4ka555 [31]

Answer:

The given functions are not same because the domain of both functions are different.

Step-by-step explanation:

The given functions are

f(x)= \sqrt{\dfrac{x+1}{x-1}}

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

First find the domain of both functions. Radicand can not be negative.

Domain of f(x):

\dfrac{x+1}{x-1}>0

This is possible if both numerator or denominator are either positive or negative.

Case 1: Both numerator or denominator are positive.

x+1\geq 0\Rightarrow x\geq -1

x-1\geq 0\Rightarrow x\geq 1

So, the function is defined for x≥1.

Case 2: Both numerator or denominator are negative.

x+1\leq 0\Rightarrow x\leq -1

x-1\leq 0\Rightarrow x\leq 1

So, the function is defined for x≤-1.

From case 1 and 2 the domain of the function f(x) is (-∞,-1]∪[1,∞).

Domain of g(x):

x+1\geq 0\Rightarrow x\geq -1

x-1\geq 0\Rightarrow x\geq 1

So, the function is defined for x≥1.

So, domain of g(x) is [1,∞).

Therefore, the given functions are not same because the domain of both functions are different.

4 0
3 years ago
(GIVING BRAINLIEST!!!!!!)<br><br> Solve 1 ÷ 1/2 = ________<br><br> A) 2<br> B) 3<br> C) 4<br> D) 5
Tcecarenko [31]

Answer:

B

Step-by-step explanation:

Becuase 1 divide 1/2

You make the division sign a multiplication sign

1 time 1/2

get the recipricol of 1/2 wich is 2

1 times 2/1

is 2

5 0
3 years ago
If a cone shaped vase can hold 45 cubic centimeter of water and has a radius of 2 centimeters what is the height of the vase use
xz_007 [3.2K]

Answer:

The height of the vase is h=10.75\ cm

Step-by-step explanation:

we know that

The volume of a cone is equal to

V=\frac{1}{3}\pi r^{2} h

we have

V=45\ cm^{3}

r=2\ cm

\pi =3.14

substitute and solve for h

45=\frac{1}{3}(3.14)(2)^{2} h

135=(3.14)(4)h

135=12.56h

h=135/12.56

h=10.75\ cm

3 0
3 years ago
1. (5x2-2x+3) + (x2+x+2)
antiseptic1488 [7]
The answer is: x^2-x+15
3 0
2 years ago
The price of an item yesterday was $40. Today, the price fell to $22. Find the percentage decrease.
klio [65]

Answer:

45%

Step-by-step explanation:

40 * .45 = 18

40-18 = 22

7 0
3 years ago
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