Question

Find the inverse of

f(x) = -6xˆ2 + 24x - 100

Answer 1

See below

Explanation:

y = -6x^2 + 24x-100

solve for 'x'

y + 100 = -6x^2 + 24x = -6(x^2-4x) complete the square for x

(y+100) /(-6 ) = (x-2)^2 -4 add 4 to both sides

(y+100)/(-6) +4 = (x-2)^2 sqrt both sides

sqrt [ ( y+100)/(-6) + 4 ] + 2 = x change x and y

y = ± sqrt [ (x+100)/(-6) + 4 ] + 2 simplify (if needed)

y = ± sqrt( -x/6 -12.666) + 2