Which function is the inverse of f(x) = (x − 3)^3 + 2?

A. f^-1(x) = ^3sqrt(x - 2) + 3

B. f^-1(x) = ^3sqrt(x + 3) - 2

C. f^-1(x) = ^3sqrt(x + 2) - 3

D. f^-1(x) = ^3sqrt(x - 3) + 7

A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.

What is the inverse of a function?

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'

The inverse fo the given function f(x) = (x − 3)³ + 2 is,

f(x) = (x − 3)³ + 2

Replace f(x) with y,

y = (x-3)³ + 2

Solve the equation for x,

y - 2 = (x - 3)³

∛(y-2) = x - 3

3 + ∛(y-2) =x

Interchange x with y and vice-versa,

y = 3 + ∛(x-2)

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Which function is the inverse of f(x) = (x − 3)^3 + 2? A. f^-1(x) = ^3sqrt(x - 2) + 3 B. f^-1(x) = ^3sqrt(x + 3) - 2 C. f^-1(x) = ^3sqrt(x + 2) - 3 D. f^-1(x) = ^3sqrt(x - 3) + 7

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What is the inverse of a function?

Otras preguntas

Which function is the inverse of f(x) = (x − 3)^3 + 2?

A. f^-1(x) = ^3sqrt(x - 2) + 3

B. f^-1(x) = ^3sqrt(x + 3) - 2

C. f^-1(x) = ^3sqrt(x + 2) - 3

D. f^-1(x) = ^3sqrt(x - 3) + 7