(2) For this problem, consider the real function

f:R->R

given by

f(x)=sin(x)

.\ (a) Is

f

injective?\ (b) Is

f

surjective?\ (c) If

W={0,\\\\pi }

, what is

f[W]

?\ (d) If

W=[0,\\\\pi ]

, what is

f[W]

?\ (e) What is

f^(-1)(1)

? What is

f^(-1)(\\\\pi )

?\ (f) If

Z=[0,1]

, what is

f^(-1)[Z]

?\ (g) Find two different intervals

x_(1),x_(2)subR

such that

f|_(x_(1)):x_(1)->[-1,1]

| and

f|_(x_(2)):x_(2)->[-1,1]

| are bijections.

(2) For this problem, consider the real function f:RR given by f(x)=sin(x). (a) Is f injective? (b) Is f surjective? (c) If W={0,}, what is f[W] ? (d) If W=[0,], what is f[W] ? (e) What is f1(1) ? What is f1() ? (f) If Z=[0,1], what is f1[Z] ? (g) Find two different intervals X1,X2R such that fX1:X1[1,1] and fX2:X2[1,1] are bijections. (2) For this problem, consider the real function f:RR given by f(x)=sin(x). (a) Is f injective? (b) Is f surjective? (c) If W={0,}, what is f[W] ? (d) If W=[0,], what is f[W] ? (e) What is f1(1) ? What is f1() ? (f) If Z=[0,1], what is f1[Z] ? (g) Find two different intervals X1,X2R such that fX1:X1[1,1] and fX2:X2[1,1] are bijections