strugglin on this question

[phantomanthrac]

Show if given functions are inverse by using f(g(x)). F(x)=3x+4 and g(x) 1/3x -4/3

 

[Deleted member 4993]

Show if given functions are inverse by using f(g(x)). F(x)=3x+4 and g(x) 1/3x -4/3

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this problem.

 

[Dr.Peterson]

Show if given functions are inverse by using f(g(x)). f(x)=3x+4 and g(x)=1/3x -4/3

To show that functions f and g are inverses of one another, you need to show that f(g(x)) = x for all x. So please show us your expression for f(g(x)) in this case, so we can see if that is where you need help.

 

[HallsofIvy]

Actually you need to show both that f(g(x))= x and g(f(x))= x. Often the one implies the other but not always.

 

[Dr.Peterson]

Actually you need to show both that f(g(x))= x and g(f(x))= x. Often the one implies the other but not always.

Yes, and I almost said that; but it specifically says, "by using f(g(x))", asking only for that half; and I specifically said, "you need to show", carefully referring to the OP, not to people outside this particular assignment. I would have said the rest later in the conversation, if it reaches that point.

 

[HallsofIvy]

Very good. Thank you.

 

[Steven G]

The job of f(x) is to triple what is between the parenthesis and then to add 4.

So if someone happens to put g(x), ie (1/3)x - (4/3), between the parenthesis then triple it and add 4. So what do you get when you triple (1/3)x - 4/3? And then after adding 4 you get? So are f and g inverses?