1.

Let f: R to R be defined as f(x) = x^(4) . Choose the correct answer.

Answer»

`f` is one-one onto
`f` is many-one onto
`f` is one-one but not onto
`f` is NEITHER one-one nor onto

Solution :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`
`thereforef` 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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