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MissTica
4 years ago
9

What is the domain and range of : y=(1/3)^x

Mathematics
1 answer:
loris [4]4 years ago
6 0
X can be any number, so the domain is all real numbers (-∞, +∞)
y is always larger than 0 in this case, so the range is all real numbers larger than 0 (0, +∞)
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consider the function and then use calculus to answer the questions that follow 1 1/x 5/x^2 1/x^3 (a) Find the interval(s) where
boyakko [2]

Answer:

a)X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)

b)Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0  )

Step-by-step explanation:

From the question we are told that

The Function

f(x)=1+\frac{1}{x}  +\frac{5}{x^2} +\frac{1}{x^3}

Generally the differentiation of function f(x) is mathematically solved as

f(x)=1+\frac{1}{x}  +\frac{5}{x^2} +\frac{1}{x^3}

f(x)=\frac{x^3+x^2+5x+1}{x^2}

Therefore

f'(x)=\frac{x^2+10x+3}{x^4}

Generally critical point is given as

f'(x)=0

\frac{x^2+10x+3}{x^4}=0

x=-5 \pm\sqrt{22}

Generally the maximum and minimum x value for critical point is mathematically solved as

f'(-5 \pm\sqrt{22})

Where

Maximum value of x

f'(-5 +\sqrt{22})

Minimum value of x

f'(-5 +\sqrt{22})

Therefore interval of increase is mathematically given by

f'(-5 -\sqrt{22}),f'(-5 +\sqrt{22})

f(x)

Therefore interval of decrease is mathematically given by

(-\infty,-5 -\sqrt{22}),f'(-5 +\sqrt{22},0),(0,\infty)

Generally the second differentiation of function f(x) is mathematically solved as

f''(x)=\frac{2(x^2+15x+6)}{x^5}

Generally the point of inflection is mathematically solved as

f''(x)=0

x^2+15x+6=0

Therefore inflection points is given as

x=\frac{1}{2} (-15 \pm \sqrt{201}

f''(x)>0,\frac{1}{2}(-15-\sqrt{201})

a)Generally the concave upward interval X is mathematically given as

X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)

f''(x)

b)Generally the concave downward interval Y is mathematically given as

Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0  )

5 0
3 years ago
Make b the subject a= 1/4 b
dalvyx [7]

<u>Answer</u>:

b =  4a

<u>Step-by-step explanation</u>:

a = \frac{b}{4}

b =  4a

<em>changing sides changes sign division to multiplication.</em>

3 0
2 years ago
Read 2 more answers
Find the distance of ST given, S ;-2,4) and T (4,1)
Angelina_Jolie [31]
You have to use the distance formula which is:

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Using the coordinates given.

D = √(4 - (-2)^2 + (1 - 4)^2

D = √(6)^2 + (-3)^2

D = √36 + 9

D = √45

D = √9 × 5

D = 3√5
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3 years ago
Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below.
egoroff_w [7]
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7 0
4 years ago
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Can somebody please help me with this?
kenny6666 [7]
بفلحلعقهقت وسريريا ليرصد في ب س
8 0
2 years ago
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