Question

Please help............................

Danika concludes that the following functions are inverses of each other because f(g(x)) = x. Do you agree with Danika? Explain your reasoning.
f(x) = |x|
g(x) = –x

Answer 1

replace the x in f(x) by the expression for g(x). What do you get

Answer 2

so i would have to solve for g(x)?

Answer 3

Just replace the x in f(x) by g(x)

that will give you an expression for f{(g)x)

Answer 4

To give you a simple example
if f(x) = x -1 and g(x) = 2x then f(g(x)) = 2x - 1

Answer 5

so x will be one right?

Answer 6

No x is just a variable and can be any real value

Answer 7

so it could be any number then

Answer 8

yes
but we are not solving an equation here
we want to see if f(g(x)) for the given f(x) and g(x) equals x.

Answer 9

okay, so f(g(x)) will have to give me a number?

Answer 10

try doing it this way

f(x) = |x|
let y = f(x)
so y = |x|

Now solve for x

Answer 11

that this equation will give me a number right?

Answer 12

no
it will give you an expression in x

Answer 13

* in y

Answer 14

i dont get it :(

Answer 15

sorry but i have to go right now
I'm sure youll get help from another person

Answer 16

thank you anyway really appreciate it

Answer 17

derp