Find the inverse function of $g(x)=-4x+1$.
So I replace $g(x)$ with $y$, then solve for $x$:
$$ 4x=1-y\\ x = \frac{1-y}4\\ y = \frac{1-x}4$$ The answer was $g(x)^{-1} =(-1/4)x + 1/4$.
Problem #12: http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Function%20Inverses.pdf
$$g(x)=-4x+1\\ \mbox{Let $g(x)=y$. Then, }-4x=y-1\\ x=(y-1)/(-4)\\ x=\dfrac{1-y}{4}\\ \boxed{g^{-1}(x)=\dfrac{1-x}{4}}$$ Or, simplifying, $$g^{-1}(x)=\dfrac{1-x}{4}\\ g^{-1}(x)=\dfrac{1}{4}-\dfrac{x}{4}=\dfrac{1}{4}-\dfrac{1}{4}x\\ \boxed{g^{-1}(x)=-\dfrac{1}{4}x+\dfrac{1}{4}}$$