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 \[y=f\,(x)\] |
\[\therefore \] \[{{f}^{-1}}(y)=x\] |
\[{{f}^{-1}}'\,(y)\,\,.\,\,y'=1\] |
\[{{f}^{-1}}''\,(y)=-\frac{y''}{{{(y')}^{2}}}\] |
\[\because \] \[y'<0\] & \[y''>0\] |
\[\therefore \] \[{{f}^{-1}}'\,(y)<0\] & \[{{f}^{-1}}''\,(y)>0\] |
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