Determinf^-1(x)

Question

Determinf^-1(x)given f(x)=3sqrt (3x+4)

Answer 1

y = 3sqr(3x+4)

switch x and y and solve for the new y

x = 3sqr(3y+4)

x^2 = 9(3y+4)

3y+4 = x^2/9

3y = x^2/9 -4

y = f^-1(x) = (x^2/9 -4)/3

f(x) = 3sqr(3x+4)> or = 0 is the top half of a rightward opening parabola, with vertex (-4/3, 0)

f^-1(x)=(x^2/9-4)/3=x^2/27 - 4/3 is an upward opening parabola with vertex (0, -4/3) = vertex of f(x) with x and y coordinates switched.

but restrict the domain of f^-1(x) to x> or = 6 to get only the right side of the parabola which is inverse of the top half of f(x), the rightward opening parabola