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# Let F: R → R Be Defined As F(X) = X4. Choose the Correct Answer. F Is One-one onto (B) F Is Many-one Ontof Is One-one but Not onto (D) F Is Neither One-one Nor onto - CBSE (Commerce) Class 12 - Mathematics

#### Question

Let fR → R be defined as f(x) = x4. Choose the correct answer.

(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

#### Solution

fR → R is defined as f(x) = x^4

Let x∈ R such that f(x) = f(y).

 =>x^4 = y^4

=> x=+-y

∴f(x_1) = f(x_2) does not imply that x_1 = x_2

For instance,

f(1) = f(-1) = 1

∴ f is not one-one.

Consider an element 2 in co-domain R. It is clear that there does not exist any x in domain R such that f(x) = 2.

∴ f is not onto.

Hence, function f is neither one-one nor onto.