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Let f: R rArr R be defined as f(x)= x^(4...

Let `f: R rArr R` be defined as `f(x)= x^(4)`. Choose the correct option

A

`f` is one-one onto

B

`f` is many-one onto

C

`f` is one-one but not onto

D

`f` is neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
D
In `f : R to R, f(x) = x^(4)`
Let `x, y in R and f(x) = f(y)`
`rArr " " x^(4) = y^(4) rArr x = pm y`
`therefore f` is not one-one.
`rArr f` is many one.
Again let `f(x) =y ` where `y in R`
`rArr " " x^(4) = y `
`rArr " " x = (y)^(1//4) notin R if y = -1 `
`therefore f ` is not onto.
Therefore, `f` is neither one-one nor onto.
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