Saved Bookmarks
| 1. |
Let f:RtoR, defined by f(x)={{:(1",",ifx""inQ),(-1",",ifx""inQ):} Find (i) f(1)/(2) (ii) f(0.34) (iii) f(sqrt2) (iv) f(pi) (v) range(f) (vi) f^(-1)(1) (vii) f^(-1){1} |
|
Answer» Solution :Since each one of `(1)/(2)` and 0.34 is rational, we have (i) `f((1)/(2))=1AND(II)f(0.34)=1`. Since each one of `sqrt2andphi` is IRRATIONAL, we have (iii) `f(sqrt2)=-1and(IV)f(pi)=-1`. (v) range `(f)={f(x):x""inR}` `={f(x):x""INQ}uu{f(x):x""inR-Q}={1,-1}`. (vi) `f^(1){1}={x:f(x)=1}=Q`. (vii) `f^(1){-1}={x:f(x)=-1}=(R-Q)`. |
|