Many One Function

Q. The function $f\left(x\right)=\frac{x^2+4x+30}{x^2-8x+18}$ is

1. both one-one and onto
2. many one
3. onto
4. one-one

Q.

Evaluate the Integral $\int {\mathrm{xsec}}^2\left(\mathrm{x}\right)\mathrm{d}x$

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

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

Q.

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

1. True

2. False

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. one – one and into
4. many – one and onto

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. Which one of the following function is not invertible?

1. $f:R\to R,f\left(x\right)=3x+1$
2. $f:R\to [0,\infty ),f\left(x\right)=x^2$
3. $f:R^{+}\to R^{+},f\left(x\right)=\frac{1}{x^3}$
4. $Noneoftheabove$

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