Find the inverse function of f(x)=x^3+2?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

f(x)=x^3+2

To find the inverse function f(x)^-1 , we will assume"

y=x^3+2

y-2= x^3

==> x= (y-2)^1/3

==> f(x)-1= (x-2)^1/3

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To find the inverse function of f(x) = x^3+2.

Solution:

Let y = x^3+2. So,

y-2 = x^3. Or

x^3 = y-2. Taking cube root,

x = (y-2) ^(1/3).

Interchanging x and y , we get:

y = (x-2)^(1/3) is the inverse function of the given function.

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

For the beginning, we'll write:f(x)=x^3+2 as y=f(x)=x^3+2

Now, we'll solve this equation for x:

y-2=x^3

x=(y-2)^1/3

Now, we'll interchange x and y:

y=(x-2)^1/3

So, the inverse function is:

[f(x)]^(-1) = (x-2)^1/3

 

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