Question

Could someone tell me how to find the inverse of g(x)= x^2-5x-6

Answer 1

rewrite as
y = x^2 - 5x - 6

Step1: interchange the x and y variables
so
x = y^2 - 5y - 6

Step2: solve this new equation for y.
in this case you will have to solve it as a quadratic in y.
rewrite as
y^2 - 5y - 6 - x = 0
and a=1, b=-5 and c=(-6-x)

y = [5 ± √(25+4(6+x))]/2
= (5 ±√(49+4x))/2

g^-1(x) = (5 ±√(49+4x))/2

You can always test your answers by starting with any x, say x = 3
g(3) = 9 - 15 - 6 = -12

then putting that value of -12 back into the second relation should give you back the 3
g^-1(-12) = (5 ±√(49+4(-12)))/2
= (5 ± 1)/2 = 3 or 2

Notice that while the first was a function, the inverse is no longer a function.

Answer 2

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