Respuesta :

RealNfw

Answer:

To determine the inverse of function f, change f(x) to y, switch x and y, and solve for y.

[tex]\frac{1}{8} (x-4)^3[/tex]

Step-by-step explanation:

f(x) = [tex]\sqrt[3]{8x} +4[/tex]

Change f(x) to y: y = [tex]\sqrt[3]{8x} +4[/tex]

Switch x and y: x = [tex]\sqrt[3]{8y} +4[/tex]

Solving for y: x - 4 = [tex]\sqrt[3]{8y}[/tex]

(x-4)^3 = 8y

y = [tex]\frac{1}{8}[/tex][tex](x-4)^3[/tex]

Therefore: inverse of function f = [tex]\frac{1}{8} (x-4)^3[/tex]

The inverse function of f(x) will be f⁻¹(x) = 1/8(x - 4)³.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) is given below.

f(x) = ∛(8x) + 4

Then the inverse function of f(x) will be

Put x = f⁻¹(x) and f(x) = x. Then we have

            x = ∛{8f⁻¹(x)} + 4

∛{8f⁻¹(x)} = x - 4

Cube on both sides, then we have

8f⁻¹(x) = (x - 4)³

 f⁻¹(x) = 1/8(x - 4)³

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Otras preguntas