Question

Consider the function f(x) = 3x-8,
What is the inverse of f(x) and name it g(x). I got that the answer was f^1(x) 1/3x+8/3. My teacher won't take though unless I show my work. Someone please help? I'm desperate?

Answer 1

this is the way to find the inverse

let y = 3x -8
now find x in terms of y:

3x = y - 8
x = (y-8) / 3

now repalce y by x ;-
inverse of f(x) = g(x) = (x - 8)/ 3

Answer 2

Was I correct though?

Answer 3

no

Answer 4

oopp sorry i made a mistake!!!

it should be ( x + 8) / 3

Answer 5

or x/3 +8/3


- i've been making typos all day !!

Answer 6

so which is it...?

Answer 7

can u understand how i got the answer or do you need more detail

Answer 8

I need more detail. my answer wasn't too far from the one you got, But I got 1/3 +8/3...

Answer 9

ok

let y = 3x - 8
add 8 to both sides
y + 8 = 3x
now divide both sides by 3
(y + 8) / 3 = x
flipping the sides
x = (y + 8/ 3

f-1 (x) = (x + 8)/ 3
- this is the correct answer
another way of writing it is

x/3 + 8/3

Answer 10

each of these answers is correct - take your pick

Answer 11

How would I use function composition to show that f(x) and gx) are inverses of eachother?

Answer 12

ok if f(x) and g(x) are inverses of eavh other then f(g(x)) = x

lets check :-

f(g(x) = 3 (x+ 8)
----- - 8
3
= 3x + 24 - 24
--------------
3

= 3x /3 = x

g(f(x)) will also be = x