To determine

To find:f-1'2

Answer

f-1'2=13

Explanation

Given:fx=x3+3sin⁡x+2cos⁡x.

Concept: By Theorem 7,f-1'a=1f'f-1a. Therefore,f-1'2=1f'f-12.

f'x=3x2+3cos⁡x-2sin⁡x.

f(x)=3x2+3sinx+2cosxf′(x)=3x2+3cosx−2sinxf′(0)=0+3−0f′(0)=3

Also,f0=2f-12=0.

Conclusion: So,f-1'2=1f'f-12=1f'0=13.