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Sudheesh Singanamalla Grade: 12
        

if ƒ:R→R be defined by ƒ(x) : x2+1 , then find ƒ-1(17) and ƒ-1(-3).


 


Please Give detailed solution.


 


The answer is given as :


ƒ-1(17) = {-4,4} , ƒ-1(-3) = ø

6 years ago

Answers : (5)

mayur hampiholi
16 Points
										

BASICALLY U NEED TO KNW THE VERY BASIC DEF OF INVERSE FN..


IF


Y=F(X)


X=F-1(Y)


NEEDLESS TO SAY THAT FOR AN EXAMPLE:


LEY Y=2*X                    X=3 => Y=6


SO, F-1(6)=3


UNDERSTOOD????


NOW F(X)=X^2+1


F-1(17)=X     =>F(X)=17


SO X^22+1=17


SO X=+4 OR -4


SIMILARLY..........


X2+1=-3


=>X2=-4


NOT POSSIBLE

6 years ago
vikas askiitian expert
510 Points
										

f(x) = x2 + 1


f(x) = y


x = f-1(y)        .....................1


y = x2 + 1


(y-1)1/2 = x     ..............2


from eq 1


f-1(y) = (y-1)1/2


so , f-1(x) = (x-1)1/2            ,      {  for all x > = 1 }


 


f-117 = +(-)4 = {-4,4}


f-1-3 = @ , coz x cannot take any value less than 1 ...

6 years ago
Neer Varshney
76 Points
										

f(x)= x2 + 1


f(1/x)= 1/(x2+1)


f-1(x)= 1/(x2+1)


f-1(17)= 1/(x2+1)


1/17 = 1/x2+1


17= x2 + 1


x2 = 16


x= {+4.-4}


 


Similarly for -3


x2 + 1 = -3


x2  = -4


x= under root -4


imaginary no.


hence f-1(-3) = 0.


 


plz approve....

6 years ago
amit karn
21 Points
										

let  y= x2 + 1


 => x2 = y-1


 => x =  √y-1


then replace y by x we get,


     f-1 (x) = √x-1


then put the value of x.

6 years ago
Sudheesh Singanamalla
114 Points
										

Thanks a lot

6 years ago
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