Question

Please help with this problem..i'm not sure how to start it?

Answer 1

\[a=f ^{-1}(c)=x\]when \[f(x)=c\]so for the first problem\[a=f ^{-1}(c)=f ^{-1}(-13)=x, f(x)=-13=4x+9x^{17}, x=-1\]also\[(f ^{-1})'(c)=\frac{ 1 }{ f'(f ^{-1}(c)) }\]so\[(f ^{-1})'(c)=\frac{ 1 }{ f'(-1)}\]and\[f'(x)=4+9(17)(x^{16})=153x^{16}+4\]so\[(f ^{-1})'(c)=\frac{ 1 }{ 153(-1)^{16}+4}=\frac{ 1 }{ 153(1)+4 }=\frac{ 1 }{ 157 }\]