Question

if R➡️R defined by f (x)=x^3, then f is
​

Answer 1

Answer:

The inverse function of the given function is given by interchanging the x and y and finding the function (the inverse function which is now y) in terms of x.

For f(x)=x

3

Let f(x)=y⇒x=f

−1

(y)

y=x

3

x=y

3

1

∴f

−1

(y)= y

3

1

f

−1

(8)=8

3

1

=2×(1)

3

1

We know that the cube roots of unity (1) are 1,ω and ω

2

∴f

−1

(8)={2,2ω,2ω

2

}

Hence, option B is correct.

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Answer 2

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the function (the inverse function which is now y) in terms of x.

For f(x)=x

3

Let f(x)=y⇒x=f

−1

(y)

y=x

3

x=y

3

1

∴f

−1

(y)= y

3

1

f

−1

(8)=8

3

1

=2×(1)

3

1

We know that the cube roots of unity (1) are 1,ω and ω

2