Question

What is the value of g[f(4)] for the functions f(x) = 2x + 1 and g(x) = 2x - 5?

Answer 1

what does f(4) equal?

Answer 2

find f(4)

Answer 3

then substite it into g(x)

Answer 4

I don't understand....

Answer 5

when x=4, what does f(x) equal?

Answer 6

f(x) = 2x + 1

when x=4

f(4) = 2(4) + 1 = ??

Answer 7

9?

Answer 8

well, if we follow the usual multiplictaion and addition rules, then yes. f(4) = 2(4)+1 = 9

Answer 9

now, whereever you see an f(4), we can replace it by 9

Answer 10

g(f(4)) = g(9)

sooo, g(x) = 2x - 5, g(f(4)) = g(9) = 2(9)-5

Answer 11

I don't understand the answer ._.

Answer 12

you dont understand what 2(9) - 5 is???

Answer 13

g(f(4)) is a notation that i think causes alot confusion. the use of xs in both cases used to throw me for a loop. essentially you have g(x) such that x = f(4), but f(4) = 9 so determine g(9).

or, another method is to construct a new function by inserting f(x) int g(x)

2(f(x)) - 5

2(2x+1) - 5

4x+2- 5

4x - 3, is equivalent to g(f(x)); now when x=4 .... you get the same result but in a different construction: 4(4) - 3

Answer 14

its simpler just to work them separately