Tag: sets

Questions Related to sets

Let $\displaystyle f(x)=ax^{2}+bx+c,$ where $a,b,c$ are rational, and $f: Z\rightarrow Z,$ where $Z$ is the set of integers. Then $a+b$ is

business maths sets some functions and their graphs -i graphs of the form y=ax^2+bx+c introduction to sets

  1. a negative integer

  2. an integer

  3. nonintegral rational number

  4. none of these

Show answer
Correct Option: B
Explanation:

$f:Z \rightarrow Z$ is defined as $f(x)=ax^2+bx+c$

which implies for integer inputs, the function gives integer outputs.

$ \Rightarrow f(0)=c=Z _1$ ...(1) (where $Z _1$ is some integer)

Similarly, $f(1)=a+b+c=Z _2$ ...(2) (where $Z _2$ is some integer)

(2) - (1) gives $a+b =Z _2-Z _1$, which is also an integer.