if f:(- ,-1]→(0,e^5] defined by f(x)=e(x^3-3x+2) is one-one,onto many-one,onto one-one,into many-one,into give answer with explanation - Maths - Relations and Functions

Question

if f:(-∞,-1]→(0,e^5] defined by
f(x)=e(x^3-3x+2) is

one-one,onto
many-one,onto
one-one,into
many-one,into

give answer with explanation

Neha Sethi · Accepted Answer

f(-∞,-1]→(0,e5]fx=ex3-3x+2Let fx=fyex3-3x+2=ey3-3y+2x3-3x+2=y3-3y+2x3-3x=y3-3yx(x2-3)=yy2-3x≠ySo, f is not one-one
onto:
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5b12d54e4112a%20png">
Similarly try other
Regards

if f:(-∞,-1]→(0,e^5] defined by f(x)=e(x^3-3x+2) is one-one,onto many-one,onto one-one,into many-one,into give answer with explanation

if f:(-∞,-1]→(0,e^5] defined by f(x)=e^{(x^3-3x+2)}is

one-one,onto

many-one,onto

one-one,into

many-one,into

give answer with explanation