Question

find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverse
f(x)=3x-6 and g(x) x+3/6
a) f(g(x))=
b)g(f(x))=

Answer 1

is it \[f(x)=3x-6\] and \[g(x)=\frac{x+6}{3}\]? if so , they are definitely inverses

Answer 2

\(f\) says multiply by 3, subtract 6
\(g\) says add 6, divide by 3
inverse operations in reverse order

Answer 3

to find inverse you just switch the x and y values around then isolate y :o

Answer 4

The directions say to find the f(g(x)) and the g(f(x)). If you get x for both of those, that shows the functions are inverse functions.

Answer 5

\[f(g(x))=f(\frac{x+6}{3})=3(\frac{x+6}{3})-6=\text{some algebra}=x\]

Answer 6

If f(g(x)) = g(f(x)), then they are inverses.

Answer 7

really?

Answer 8

Yeah. My teacher told me.

Answer 9

Only if they are both equal to x

Answer 10

\[f(x)=2x, g(x)=3x\] \[f(g(x))=g(f(x))=6x\] i sincerely hope your teacher did not tell you that

Answer 11

@avatar2012 you job is to compute
\[f(g(x))\] and \[g(f(x))\] i wrote the first one. you will get \(x\) back for the second one as well, so they are inverses for sure

Answer 12

If they are truly inverse, such as f(x) = 2x + 6 and g(x) = (x - 6)/2, then f(g(x)) = g(f(x))
f(g(x)) = (2)(x - 6)/2 + 6 = x - 6 + 6 = x
g(f(x)) = (2x + 6 - 6)/2 = 2x/2 = x
See? x = x

Answer 13

These are not inverse because:
y = 3x - 6
x = 3y - 6
x + 6 = 3y
(x + 6)/3 = y
(x + 3)/6 ≠ (x + 6)/3

Answer 14

Do you understand?

Answer 15

thanks

Answer 16

They are inverse functions!!

Answer 17

f(x)=3x-6 and g(x) x+3/6 are inverse functions? Because satellite73 wrote it wrong.

Answer 18

y = 3x - 6
x = 3y - 6
x + 6 = 3y
(x + 6)/3 = y
(x + 3)/6 ≠ (x + 6)/3?
That's what I did.