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.

Explanation

If `f(a)=g(a)` for all `a in A` then f and g are equal.
Given `A={-1,0,1,2}` and `B={-4,-2,0,2}`
`f(x)=x^2-x,x in A `and `g(x)=2|x-1/2|-1, x in A`
Check `x=-1`
`f(-1)=(-1)^2-(-1)=2`
`g(-1)=2|x-1/2|-1=2(3/2)-1=2`
`implies f(-1)=g(-1)`
Check `x=0`
`f(0)=0^2-0=0`
`g(0)=2|0-1/2|-1=2(1/2)-1=0`
`f(0)=g(0)`
Check `x=1`
`f(1)=1^2-1=0`
`g(1)=2|1-1/2|-1=1-1=0`
`f(1)=g(1)`
Check `x=2`
`f(2)=2^2-2=4-2=2`
`g(2)=2|2-1/2|-1=2(3/2)-1=2`
`f(2)=g(2)`
Since `f(a)=g(a) AA a in A` if f and g are equal .
The statement is true,