# F(x).....

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#1
Givving that f(x) = X^2-8X

Find f^-1 (x)
0
15 years ago
#2
(Original post by KOH)
Givving that f(x) = X^2-8X

Find f^-1 (x)

just complete the square.
0
#3
(Original post by Ralfskini)
just complete the square.
I did, but cant get it
0
15 years ago
#4
(Original post by KOH)
Givving that f(x) = X^2-8X

Find f^-1 (x)
dont u have to swap x and y round to get

x=y^2-8y
x=(y-4)^2-16
(x+16)^0.5=y-4
so y=4+-sqrt(x+16)
0
15 years ago
#5
You need to restrict the domain of f to {x >= 4} to get a unique inverse. The range of f is then {y >= -16}. The domain of f^-1 is the range of f.

For all x >= 4 with y = x^2 - 8x we have

y = (x - 4)^2 - 16,
y + 16 = (x - 4)^2,
sqrt(y + 16) = x - 4,
x = 4 + sqrt(y + 16).

So f^-1(y) = 4 + sqrt(y + 16) for all y >= -16.
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