Algebraically determine the inverse of the quadratic function: f(x) = 7(x+1)^2 - 2

Question

f(x) = 7(x+1)² - 2

Answer 1

y=7(x+1)^2 - 2

to find the inverse just switch x and y, then solve for the new y

x=7(y+1)^2 -2

7(y+1)^2= x+2

y = -1+/-sqr[(x+2)/7]

or

x = 7y^2 + 14y + 5

(notice, it's an inverse relation,

but there is no inverse function as it fails the vertical line test)

or graph it,

it's an upward opening parabola with vertex = (-1,-2) stretched vertically by a factor of 7

reflect it over the line x=y to get a rightward opening parabola with vertex (-2,-1), stretched horizontally, which is the inverse relation