Question

find the inverse on the given interval and graph both f and f^-1 on the same set of axes. f(x)=x^2-8x+1 for x>=4

Answer 1

\[f(x)=(x-4)^2 -16+1\\y=(x-4)^2 -15\\x \ge4 \\(x-4)^2 \ge 0\\(x-4)^2-15 \ge -15\\so \\\\y \ge -15\\y+15=(x-4)^2 \\ \\ \sqrt{y+15}=|x-4| \\x \ge 4\\sqrt{y+15}=x-4\\so x=4+\sqrt{y+15} \\f^{-1}=4+\sqrt{x+15}\]

Answer 2

Thanks!! :)