Question

Which of the following functions is not onto

• A. $f: R \rightarrow R , f(x)=3 x+4$
• B. $f: R \rightarrow R ^{+}, f(x)=x^2+2$
• C. $f: R ^{+} \rightarrow R ^{+}, f(x)=\sqrt{x}$
• D. none of these

Answer 1

Answer: (B)

The function $f(x)=3 x+4$ is onto as for $y \in$ $R , f\left(\frac{y-4}{3}\right)=y$.
The function $f: R ^{+} \rightarrow R ^{+}, f(x)=\sqrt{x}$ is onto as for $y \in R ^{+}, f\left(y^2\right)=y \cdot f: R \rightarrow R ^{+}, f(x)=x^2+2$ is not onto as $1 \in R ^{+}$has no pre-image.