Show algebraically that f and g are inverse functions.

f(x)=9x-8 g(x)= x+8/9 (x+8 is numerator, 9 is denominator)
please make clear in work what is numerator and denominator since this is text
solution: f(g(x))=f(x+8(numerator)/9(denominator))…
g(f(x))=g(9x-8)= 9x-8+8(numerator)/9(denominator)=9x(nume…

I am obviously pretty stupid, so if anyone can explain how this works step by step i would really appreciate it

Hi,

Find the inverse of f(x) = 9x - 8, which is the same as y = 9x - 8.

Switch the x and y.

x = 9y - 8

Solve this for y.

x + 8 = 9y

x + 8
-------- = y <==This is the inverse of f(x), which happens to be g(x).
. 9

Second way to do it.

If f(x) and g(x) are inverses, then f(g(x)) = x or g(f(x)) = x

f(x) = 9x - 8

Replace x with g(x).

f(g(x)) = 9(x + 8)/9 - 8

f(g(x)) = (x + 8) - 8

f(g(x)) = x

OR

x + 8
-------- = g(x).
. 9

Replace x with f(x).

(9x - 8) + 8
----------------- = g(f(x)).
. 9


9x - 8 + 8
--------------- = g(f(x)).
. 9


9x
---- = g(f(x)).
9

x = g(f(x)).

I hope that helps!! :-)

Well, run the f(g(x)) and the g(f(x)).

f(g(x)) = f(x+8/9), wherever you see x in 9x-8, replace it with (x+8)/9, so you've got
9((x+8)/9)-8 = x+8-8=x
g(f(x)) = g(9x-8): again wherever you see x in (x+8)/9, replace it with (9x-8), which gives you ((9x-8)+8)/9 = 9x/9 = x

As long as you get x for both, they are inverses.
Whenever you do f(g(x)), remember, wherever you see x in f(x), replace it with g(x).

No, you're not stupid. It takes some getting used to. Keep your head up.

the invese function is obtained this way

y=f(x) and write x depending on y
so we have
y=9x-8
y+8=9x
(y+8)/9=x != g
conclusion g is not the inverse of f