Many One Function

Q. Let $f:R\to R$ be a mapping, such that $f\left(x\right)=\frac{x^2}{1+x^2}$ Then, f is

1. Many – one into
2. One – one
3. Onto
4. Into

Q.

All the functions are either one- one or many-one.

1. True

2. False

Q. Which of the following functions is non – injective?

1. $f\left(x\right)=|x+1|,xϵ[-1,\infty )$
2. $g\left(x\right)=x+\frac{1}{x},xϵ(0,\infty )$
3. $h\left(x\right)=x^2+4x-5,xϵ(1,\infty )$
4. $k\left(x\right)=e^{-x},xϵ[0,\infty )$

Q. $f:R\times R\to R$ such that f(x + iy) = $\sqrt{x^2+y^2}$. Then, f is

1. many – one and into
2. one-one and onto
3. many – one and onto
4. one – one and into

Q. Let $f:R\to R$ be a mapping, such that $f\left(x\right)=\frac{x^2}{1+x^2}$ Then, f is

1. Many – one into
2. One – one
3. Into
4. Onto

Q. If $f\left(x\right)=\ln x;$ where $x\in R^{+},$ then

1. $f(x+y)=f\left(x\right)+f\left(y\right)$
2. $f(x\cdot y)=f\left(x\right)+f\left(y\right)$
3. $f(x+y)=f\left(x\right)\cdot f\left(y\right)$
4. $f(x\cdot y)=f\left(x\right)\cdot f\left(y\right)$