IF f:R to R be defined as follows:
F(x)= {1, if x belongs to Q}
F(x)={-1,if x does not belongs to Q}
find
1)f(1/2),f(pi), f(root 2)
2)range of f
3)pre images of 1 and -1

Question

Neha Sethi · Accepted Answer

Dear student

f(x)=1,x∈Q-1,x∉Q1) f12=1 as 12∈Qfπ=-1 as π∉Qf2=-1 as 2∉Q2) Range of f is x∈[-1,1]3)  pre-image of 1 is 12 according to part(1)pre-image of -1 is  π and 2 according to part (1)In general pre-image of 1 is x∈Qand pre-image of -1 is x∉Q
Regards

IF f:R to R be defined as follows: F(x)= {1, if x belongs to Q} F(x)={-1,if x does not belongs to Q} find 1)f(1/2),f(pi), f(root 2) 2)range of f 3)pre images of 1 and -1

IF f:R to R be defined as follows:
F(x)= {1, if x belongs to Q}
F(x)={-1,if x does not belongs to Q}
find
1)f(1/2),f(pi), f(root 2)
2)range of f
3)pre images of 1 and -1