Question

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.

Answer 1

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

Answer 2

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?

Answer 3

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.