Functions

The figure shows a relationship between the sets $P$ and $Q.$ Write this relation in Roster form.
What is it’s domain and range?

Let $f$ be the subset of $z\times z$ defined by $f=\left\{\right(ab, a+b):a, b\in Z\}$ is $f$ a function from $z$ to $z?$ Justify your answer  

Let $R$ be a relations from $N$ to $N$ defined by $=\left\{\right(a,b):a,b\in N \mathrm{a}\mathrm{n}\mathrm{d}a=b^2\}$. Is the following true?
 $(a,b)\in R,(b,c)\in R$ implies $\left(a,c\right)\in R.$

Let $R$ be a relation from $N$ to $N$ defined by $=\left\{\right(a,b):a,b\in N \mathrm{a}\mathrm{n}\mathrm{d}a=b^2\}$. Is the following true?
 $\left(a,b\right)\in R,$ implies $\left(b,a\right)\in R$

Let $R$ be a relations from $N$ to $N$ defined by $=\left\{\right(a,b):a,b\in N \mathrm{a}\mathrm{n}\mathrm{d}a=b^2\}$.Is the following true?
 $\left(a,a\right)\in R,$ for all $a\in N$

Let $f=\left\{\left(\mathrm{1,1}\right),\left(\mathrm{2,3}\right),\left(0,-1\right),\left(-1,-3\right)\right\}$ be a function from $Z$ to $Z$ defined by $f\left(x\right)=ax+b,$ for some integers $a,b.$ Determine $a,b.$

Let $f,g:R\to R$ be defined, respectively by $f\left(x\right)=x+1,g\left(x\right)=2x-3.$ Find $f+g,f-g$ and $\frac{f}{g}.$

If $f\left(x\right)=x^2,$ find $\frac{f\left(1.1\right)-f\left(1\right)}{\left(1.1-1\right)}$

The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t\left(C\right)=\frac{9C}{5}+32.$ Find
The value of $C$ when $t\left(C\right)=212$

The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t\left(C\right)=\frac{9C}{5}+32.$ Find
 $t\left(-10\right)$

The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t\left(C\right)=\frac{9C}{5}+32.$ Find
 $t\left(28\right)$

The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t\left(C\right)=\frac{9C}{5}+32.$ Find
 $t\left(0\right)$

A function $\mathrm{f}$ is defined by $\mathrm{f}\left(x\right)=2x-5.$ Write down the values of $\mathrm{f}\left(-3\right)$

A function $f$ is defined by $f\left(x\right)=2x-5.$ Write down the values of
$f\left(7\right)$

A function $f$ is defined by $f\left(x\right)=2x-5.$ Write down the values of
 $f\left(0\right)$

Find the domain and range of the following real function:
 $f\left(x\right)=\sqrt{9-x^2}$

Find the domain and range of the following real function:
 $f\left(x\right)=-\left|x\right|$