R S Aggarwal Solutions for Exercise 1: EXERCISE 3A

Let $X=\{1,2, 3, 4\},Y=\{1, 5, 9, 11, 15, 16\}$  and  $f=\left\{\right(1, 5), (2, 9), (3, 1), (4, 5), (2, 11\left)\right\}$.

Is $f$ is a function from $X$ to $Y$ true? Justify your answer.

Let $f:R\to R:f\left(x\right)=x^2$ and $g:C\to C:g\left(x\right)=x^2$ , where $C$ is the set of all complex numbers.

Show that $f\ne g$.

$g$ is the function defined from $R to R$ as following $g\left(x\right)=\sin x$. Then, find the range.

Let $f: R\to R, f\left(x\right)=x^2+1 .$ Find$f^{-1}\left\{10\right\}$

Let $f: R\to R : f\left(x\right)=x^2+1$. Find$f^{-1}\{-3\}$.

The function $F\left(x\right)=\frac{9x}{5}+32$ is the formula to convert $x°C$to Fahrenheit units. Find $F\left(0\right)$.

The function $F\left(x\right)=\frac{9x}{5}+32$ is the formula to convert $x°C$ to Fahrenheit units. Find$F(-10)$.

The function $F\left(x\right)=\frac{9x}{5}+32$ is the formula to convert $x°C$ to Fahrenheit units. Find The value of $x$ when $F\left(x\right)=212$.