Let `A" "=" "{-1," "0," "1," "2}` , `B" "=" "{-4," "-2," "0," "2}` and `f,g:" "A" "->" "B` be functions defined by `f(x)=x^2-x ,""""x in A` and `g(x)=2|x-(1/2)|-1, x in A` . Are f and g equal? Justify your answer. (Hint: One may note that two functio

Explanation

Here A={-1, 0, 1,2}
and B={-4, -2, 0 ,2}
In f,g:`A rarr B,f(x) =x^2-x`
and `g(x)=2|x -1/2|-1, x in A`
Now `f(-1)=(-1)^2-(-1)=1+1=2`
and `g(-1)=2 |-1-1/2|-1=3-1 =2`
`therefore f(1-)=g(-1)`
`f(0) =0^2-0=0`
and g(0) =2|0-1/2|-1 = 1-2=0
`therefore f(0)=g(0)`
and `g(1)=2|1-1/2|-1=2 (1/2)-1=0`
`therefore f(1)=g(1)`
`f(2)=2^2-2=4-2=2`
`and g(2)=|2-1/2|-1=3-1=2`
`therefore f(2)=g(2)`
Therefore , `AA a in A,`
`f(a)=g(a)`
`rArr ` f and g are equal