A) decreasing and have concavity upwards
B) decreasing and have concavity downwards
C) increasing and have concavity downwards
D) increasing and have concavity upwards
Correct Answer: A
Solution :
| Let \[y=f(x)\] |
| \[\therefore {{f}^{-1}}(y)=x\] |
| \[\therefore {{f}^{-1}}(y).y'=1\] |
| \[{{f}^{-1''}}(y)=-\frac{y'}{{{(y')}^{2}}}\] |
| \[\because y'<0\]& \[{y}''>0\] |
| \[\therefore {{f}^{-1}}(y)<0\]& \[\therefore {{f}^{-1''}}(y)>0\] |
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