Question

The function $f:R\rightarrow \bigg [-\frac{1}{2}, \frac{1}{2}\bigg ]$ defined as f(x) = $\frac{x}{1+x^{2}}$, is:
(a) neither injective nor surjective
(b) invertible
(c) injective but not surjective
(d) surjective but not injective

Answer 1

The function $f:R\rightarrow \bigg [-\frac{1}{2}, \frac{1}{2}\bigg ]$ defined as f(x) = $\frac{x}{1+x^{2}}$, is:

(a) neither injective nor surjective

(b) invertible

(c) injective but not surjective

(d) surjective but not injective

Answer 2

The function f:R\rightarrow \bigg [-\frac{1}{2}, \frac{1}{2}\bigg ]f:R→[−

2

1

,

2

1

] defined as f(x) = \frac{x}{1+x^{2}}

1+x

2

x

, is:

(a) neither injective nor surjective

(b) invertible

(c) injective but not surjective

(d) surjective but not injective