Question

PLEASE HELP
Find the inverse and determine whether or not its a function:
f(x)=(8-2x)^2

Answer 1

We want to solve for x to find the inverse.
f(x)= (8 - 2x)^2
sqrt( f(x) ) = |8 - 2x|
+- sqrt( f(x) ) = 8 - 2x
8 +- sqrt( f(x) ) = -2x
- (8 +- sqrt( f(x) ))/2 = x

x = -(8 + sqrt( f(x) ))/2, and
x = -(8 - sqrt( f(x) ))/2

f(x) = -(8 + sqrt(x)) / 2, and
f(x) = -(8 - sqrt(x)) / 2

this inverse would not be a function (we could tell this from the start by horizontal line test on the original f(x), but we were asked to find the inverse anyways )

Answer 2

So do i have to graph it in order to do the horizontal line test? I just won't have my graphing calculator with me for the test on this?

Answer 3

you would probably be asked to show the graph to use the horizontal line test, so yeah
you'd just have to do it algebraically (like how I did it) to do it without graphing.

Answer 4

well how do i know if its a function without using the test

Answer 5

basically, if you get more than one equation for x (with +-'s), any x-value will correspond to two different y values, which means that the inverse cannot be a function

Answer 6

Ex) y = x^2
+- sqrt(y) = x

x = sqrt(y) and x = -sqrt(y)
y = sqrt(x) and y = -sqrt(x)

for any x, there's two y values.

Answer 7

thank you makes sense!