It's easy to prove it has an inverse however I'm unable to calculate the inverse and thus its derivate and I'm not sure how to use the inverse function rule in this case. Can anyone help?
2026-03-31 17:50:43.1774979443
Show that $x^7 + 5x^5 + 2x - 2$ has an inverse $g(x)$ and compute $g'(-2)$.
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$$f(x)=x^7+5x^5+2x-2$$ $$f^{-1}(-2)=a$$ $$f(a)=-2$$ $$a=0$$ $$(f^{-1}(-2))'=\frac{1}{f'(f^{-1}(-2))}=\frac{1}{f'(0)}$$