Question

10. Let f be a function from C (set of all complex numbers) to itself given by f (x) = x 3. Write
f-1(-1).
​

Answer 1

f(x) = x³

Let f-¹(x) = z

Now we know that

f(f-¹(x)) = x

→ f(z) = x

→ z³ = x

→ z = x^⅓

Hence, f-¹(x) = x^⅓

So,

f-¹(-1) = (-1)^⅓

= -1

Answer 2

Required Answer :

Let f -¹ (x) = z

Now , let's begin steps ,

➙f-¹(y) x

➙f(x) = -1

➙f-¹(-1) = x

➙x³ = -1

➙x³ + 1 = 0

➙(x + 1)(x² - x + 1) = 0

➙x = -1

Hence, the answer is -1