Polynomial Function

Q. Let f = {(−1, 3), (0, −1), (2, −9)} be a linear function from Z $\to$ Z . Find f (x).

1. 4x-1
2. -4x+1
3. -4x-1
4. 4x+1

Q.

Fill in the blanks:

Every linear equation in one variable has exactly ____________ solution.

Q.

Q. Find the domain and range of $f\left(x\right)=\frac{1}{(x-5)}$

Q. Let $f=\left\{\right(1,1),(2,3),(0,-1),(-1,-3\left)\right\}$ be a linear function from $Z$ into $Z$. Find $f\left(x\right)$.

Q. Find the domain and range of $f\left(x\right)=\sqrt{\frac{x-5}{3-x}}$

1. Domain of $f\left(x\right)=R-\left[0\right]$

   Range of $f\left(x\right)=[0,5]$

2. Domain of $f\left(x\right)=R-\left[0\right]$

   Range of $f\left(x\right)=[5,\infty )$

3. Domain of $f\left(x\right)=R-\left[3\right]$

   Range of $f\left(x\right)=[0,5]$

4. Domain of $f\left(x\right)=R-\left[3\right]$

   Range of $f\left(x\right)=[5,\infty )$

Q. Polynomial function is a superset of which of the following functions?

1. Constant function
2. Linear function
3. Quadratic function
4. Modulus function

Q. Find the domain and range of $f\left(x\right)=\frac{1}{\sqrt{x^2-1}}$.

1. Domain of $f\left(x\right)=(\infty ,-1)$

   Range of $f\left(x\right)=(0,\infty )$

2. Domain of $f\left(x\right)=(\infty ,-1)\cup (1,\infty )$

   Range of $f\left(x\right)=(0,1)$

3. Domain of $f\left(x\right)=(1,\infty )$

   Range of $f\left(x\right)=(0,\infty )$

4. Domain of $f\left(x\right)=(\infty ,-1)\cup (1,\infty )$

   Range of $f\left(x\right)=(0,\infty )$

Q. f(x) is a linear function. If f(1) = 2 and f(3) = 8, then f(x) = .

1. 3x - 1
2. 2x + 1
3. 3x + 1

Q. If $f\left(x\right)=\frac{kx}{x+1}$ where $x\ne -1$ and $f\left\{f\right(x\left)\right\}=x$ for $x\ne 1$ then find the value of $k$.

Q. Find the domain and range of $f\left(x\right)=\sqrt{3x-5}$.

Q. Let $f:R\to R$ be defined by $f\left(x\right)=\frac{x+1}{x^2+2},x\in R$.Find $f\left(7\right)$

Q. Find the domain and range of $f\left(x\right)=\frac{1}{\sqrt{2x-3}}$.

1. Domain of $f\left(x\right)=(\frac{1}{2},\infty )$

   Range of $f\left(x\right)=[\frac{1}{2},\infty )$

2. Domain of $f\left(x\right)=(\frac{3}{2},\infty )$

   Range of $f\left(x\right)=[\frac{3}{2},\infty )$

3. Domain of $f\left(x\right)=(\frac{3}{2},\infty )$

   Range of $f\left(x\right)=[\frac{1}{2},\infty )$

4. Domain of $f\left(x\right)=(\frac{1}{2},\infty )$

   Range of $f\left(x\right)=[\frac{3}{2},\infty )$

Q. $f\left(x\right)=x^2+2$ is a quadratic function.

1. True
2. False