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
[tex]6y^3=x-10[/tex]
[tex]y^3=\frac{x-10}{6}[/tex]
[tex]y=^{\sqrt[3]{\frac{x-10}{6}}}[/tex]
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
[tex]4y^3=x-5[/tex]
[tex]y^3=\frac{x-5}{4}[/tex]
[tex]y=^{\sqrt[3]{\frac{x-5}{4}}}[/tex]
By comparing with given inverse function.
Its clear its the correct option.
C).
Given function: f(x) = [tex]^{\sqrt[3]{x+3}}-5[/tex]
To find inverse first put y = f(x) then interchange y & x and solve for y
y = f(x)
x = f(y)
[tex]x=^{\sqrt[3]{y+3}}-5[/tex]
[tex]x+5=^{\sqrt[3]{y+3}}[/tex]
[tex](x+5)^3=y+3[/tex]
[tex](x+5)^3-3=y[/tex]
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
[tex]y=\frac{^{\sqrt[3]{x}}+3}{4}[/tex]
By comparing with given inverse function.
Its clear its not the correct option.
Therefore, Pair of function Option B is Inverse of Each other.
