Question

what is the inverse of this function X^2 +5x-6 if x<0 I am struggling with the x^2 + 5x part please help

Answer 1

let f(x)= X^2 +5x-6
let y=f(x)
y= X^2 +5x-6
complete the square
and make x the subject

Answer 2

I don't know how to complete the square the rest I can do the the spuare is confusing

Answer 3

i know x^2+5x-6 = (x+6) (x-1)

Answer 4

you factorised it, which will not help us, if we complete the square we can get x on its own.
to complete the square you want to do x plus half the coefficient of x
square it
then take away the square
so like this...
X^2 +5x-6
you do
(x+5/2)^2 - (5/2)^2 -6
the negative 6 just stays there

so now you have
y=(x+5/2)^2 -(5/2)^2 - 6
can you do this from here?

Answer 5

then the last step is (x+2.5)^2-12.25 ?

Answer 6

yes then make x the subject
once you do that, you replace the x with f^1(x)
and replace your y with x
to get your inverse function
I must go to school now, but will check what answer you get in 30 mins

Answer 7

thanks a lot x= (9y+12.25)^0.5 -2.5

Answer 8

why did you get 9y?

Answer 9

you should get
x=(y+12.25)^0.5 -2.5
then finish of by replacing x with f^-1(x)
and replacing y with x
to get
F^-1(x)= (x+12.25)^0.5 -2.5

Answer 10

thanks for all the trouble