Question

Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______ 

Options

• Neither one-one nor onto

• One-one

• Onto

• One-one onto

Answer 1

Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be Neither one-one nor onto.

Explanation:

Let x₁ = 0°, X₂ = 180°, then f(0°) = sin (0°) = 0 and f(180°) = sin (180°) = 0

Now f(x₁) = f(x₂) but x₁ ≠ x₂,

∴ it is not one-one.

Again the value of f-image of x lies in between -1 to 1

⇒ f[R] = {f(x) : -1 ≤ f(x) ≤ 1)}

So other numbers of co-domain (besides -1 and 1) are not f-image. f[R] ∈ R, so it is also not onto.

So this mapping is neither one-one nor onto.