Posted by **Diana** on Friday, July 15, 2011 at 4:21pm.

How would you find the inverse of these two functions: f(x)=4/(x-4)^2 and

f(x)=x^2-8x+16

could you please show me step by step i have been trying to figure it out for hours.

- precalc -
**Reiny**, Friday, July 15, 2011 at 5:32pm
first one:

y = 4/(x-4)^2

inverse is

x = 4/(y-4)^2

solving this for y .....

(y-4)^2 = 4/x

y - 4 = ± 2/√x

y = 4 ± 2/√x

2nd .....

inverse is

x = y^2 - 8y + 16

y^2 - 8y + 16 - x = 0

use the quadratic equation

where a=1, b=-8 and c = 16-x to solve for y

- precalc -
**Diana**, Friday, July 15, 2011 at 5:50pm
thanks i got the first one now!

for the second one I used the quadratic eqn and got 4 but that is not the answer?

- precalc -
**Reiny**, Friday, July 15, 2011 at 5:59pm
y = (8 ± √(64-4(1)(16-x))/2

= (8 ± √(4x) )/2

= (8 ± 2√x)/2

= 4 ± √x

check: let x = 3 into the first

y = 9 - 24 + 16 = 1

put x = 1 into the second:

y = 4 ± √1 = 5 or 3

notice the the inverse of each of the equations is not a function.

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