Pre-Calculus Equation

Question

f(X) = √x is translated 2 units right and 5 units down to create g(x). What equation represents g-1(x)

Answer 1

f(x) = sqrx translate right 2, down 5

g(x) = sqr(x-2) - 5

both f and g are the top half of a horizontal rightward opening parabola

g has vertex (2,-5) and x intercept = 27 and no y intercept

f has vertex (0,0) and x intercept = 0 = y intercept

g^-1(x) is the inverse of g(x0

y =sqr(x-2)-5 switch x and y and solve for the new y

x = sqr(y-2)-5

sqr(y-2) = x+5

y-2 = x^2 +10x +25

y = x^2 +10x +27 = g^-1(x)

which is a vertical upward opening parabola with y intercept =27

(x+5)^2 +2 has vertex (-5,2)