Question

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

Answer 1

Answer:

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 2

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