Question

f(x) = 10-x and g(x) = 5x+6 ,

find the following:

a) f(g(x))

b) g(f(x))

c) f(f(x))

Answer 1

Just giving me an example of a) Is fine too im just trying to figure out how to set it up and solve it ^^

Answer 2

f(g(x)) means to simply put the expression, g(x), into f(x) in place of all instances of the variable x. Think of it like a search-and-replace, where every x in the "outer function" (in this case, f(x)) is replaced by the inner function, in this case (5x + 6).

So you get f(g(x)) = 10 - (5x + 6) = 4 - 5x

Now can you try the other 2?

Answer 3

f(g(x)) just applies you put the function g(x) where ever there is an x in f(x). So, \[f(g(x)) = 10-(5x+6)\] do so similarly with others.

Answer 4

@DebbieG Ok so you got 4 - 5x by 10 - 6 and 5x being by it self? so b) would be
5(10 - x) + 6 = 50x + 6 ?

Answer 5

Your distribution is wrong, but yet you get the point :)

Answer 6

yes*

Answer 7

\[g(f(x)) = 5(10-x)+6 \implies 50-5x+6\]

Answer 8

Yes, 5(10 - x) + 6, but 5(10 - x) + 6 != 50x + 6

I don't really understand what you mean by, "Ok so you got 4 - 5x by 10 - 6 and 5x being by it self?"

Answer 9

@DebbieG I was trying to see if i understood how you did it with my way of explaining how i took what you did. If that clears it up

Answer 10

@Astrophysics Ok so would that mean f(f(x)) 10 - (10 - x) = 10 - 10x?

Answer 11

\[f(f(x)) = 10 - (10-x)\]

Answer 12

@Astrophysics Thank you so much ^^ That was easier then i thought lol

Answer 13

Note that there is a "negative 1" there