Answer:
-1
Step-by-step explanation:
Note that by definition,
[tex]f(g(x))=x \implies f'(g(x)) g'(x) = 1 \implies g'(x)=\frac{1}{f'(g(x))}[/tex]
Substituting x=1,
[tex]g'(1)=\frac{1}{f'(g(1))}[/tex]
As g is the inverse of f,
[tex]f(-1)=1 \implies g(1)=-1 \\ \\ \implies g'(1)=\frac{1}{f'(-1)}[/tex]
By the power rule, f'(x)=2x+1, so f'(-1)=-1.
[tex]\implies g'(1)=\frac{1}{-1}=-1[/tex]
