Question

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

Answer 1

i think it would be B i think i am wrong though

Answer 2

Pair of function Option B is Inverse of Each other.

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=(x-10)/(6)`

`y=^{\sqrt[3]{(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=(x-5)/(4)`

`y=^{\sqrt[3]{(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.