Question

Which function is the inverse of ƒ(x) = 4x3 – 2?

Answer 1

To find:-

• The inverse of f(x) = 4x³ - 2 .

Answer:-

Given function to us is ,

`\implies f(x) = 4x^3 - 2 \\`

Replace f(x) with y as ,

`\implies y = 4x^3 - 2 \\`

Interchange x and y , and then solve for y to find out the inverse.

`\implies x = 4y^3 - 2 \\`

`\implies x + 2 = 4y^3 \\`

`\implies 4y^3 = x + 2 \\`

`\implies y^3=(x+2)/(4) \\`

`\implies y =\sqrt[3]{(x+2)/(4)} \\`

Replace
`y = f^(-1)(x)`

`\implies \underline{\underline{ f^(-1)(x) = \sqrt[3]{(x+2)/(4)} }} \\`

and we are done!

Answer 2

Answer: C

Explanation:

Rewrite the equation as: y=4x³-2

Swap x & y:

x=4y³-2

Solve for y:

x+2=4y³

(x+2)/4=y³

last step i can't show in here