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```
if ƒ:R→R be defined by ƒ(x) : x 2 +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

```
9 years ago

```							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
```
9 years ago
```							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 ...
```
9 years ago
```							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....
```
9 years ago
```							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.
```
9 years ago
```							Thanks a lot
```
9 years ago
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