Mathematics, 21.07.2019 02:40 denisefaircloth73

Which of the following pairs of functions are inverses of each other

Answers: 2

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Answer from: juniorcehand04

Pair of function Option B is Inverse of Each other.

Step-by-step explanation:

A).

Given function: f(x) = 6x³ + 10

To find inverse first put y = f(x) then interchange y & x and solve for y

y = f(x)

x = f(y)

x = 6y³ + 10

6y^3=x-10

$y^3=\frac{x-10}{6}$

$y=^{\sqrt[3]{\frac{x-10}{6}}}$

By comparing with given inverse function.

Its clear its not the correct option.

B).

Given function: f(x) = 4x³ + 5

To find inverse first put y = f(x) then interchange y & x and solve for y

y = f(x)

x = f(y)

x = 4y³ + 5

4y^3=x-5

$y^3=\frac{x-5}{4}$

$y=^{\sqrt[3]{\frac{x-5}{4}}}$

By comparing with given inverse function.

Its clear its the correct option.

C).

Given function: f(x) = $^{\sqrt[3]{x+3}}-5$

To find inverse first put y = f(x) then interchange y & x and solve for y

y = f(x)

x = f(y)

$x=^{\sqrt[3]{y+3}}-5$

$x+5=^{\sqrt[3]{y+3}}$

(x+5)^3=y+3

(x+5)^3-3=y

By comparing with given inverse function.

Its clear its not the correct option.

D).

Given function: f(x) = (4x-3)³

To find inverse first put y = f(x) then interchange y & x and solve for y

y = f(x)

x = f(y)

x = (4y-3)³

4y-3 = ∛x

4y = ∛x + 3

$y=\frac{^{\sqrt[3]{x}}+3}{4}$

By comparing with given inverse function.

Its clear its not the correct option.

Therefore, Pair of function Option B is Inverse of Each other.

Answer from: Quest

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

Answer from: Quest

what do u need to know

step-by-step explanation: