Question

Each letter of the alphabet is assigned a numerical value according to its position in the alphabet. Encode the message SEND âHELP, using theâ one-to-one function defined by f(x) = x^3 - 1. Give the inverse function that the decoder would need when the message is received.Write the encoded message. Use space to separate the numbers?
The inverse function is:_________.
f -1 (x) = ?

Answer 1

Answer:

f⁻¹(x) = ∛(x+1)

Step-by-step explanation:

Given the encoded message defined by the function f(x) = x³-1,  the inverse function that the decoder would need when the message is received can be expressed as thus:

let the inverse of the function be represented as y such that y = x³-1.

Making x the subject of the formula from the equation above;

x³ = y+1

Taking the cube root of both sides:

∛x³ = ∛(y+1)

x = ∛(y+1)

replacing y with x:

y = ∛(x+1)

f⁻¹(x) = ∛(x+1)

The encoded message is the inverse function ∛(x+1)