Question 262565
here is the original equation:
{{{f(x)= sqrt((x^2)+8x)}}}
let f(x) = y and then reverse all x and y variables to get
{{{x= sqrt((y^2)+8y)}}}
step 1 - square both sides to get
{{{x^2 = y^2 + 8y}}}
now x^2 is a constant, so we can set = 0 as
{{{y^2 + 8y - x^2 = 0}}}
using the quadratic formula, we get
{{{y = (-8 +- sqrt(64 + 4*1*x^2))/2}}}
factor a 4 out of the sqrt to get
{{{y = (-8 +-2sqrt(16+x^2))/2}}}
reduce to get
{{{y^(-1) = (-4 +-sqrt(16+x^2))}}}