Question

Let..... (will draw what to let in a sec!)

Which of the following could be a possible decomposition of h(x)?

(will post answer choices in a sec also!)

***PLease explain!! Thank youuu :D

Answer 1

answer choices A,B,C,D top to bottom :)

Answer 2

(g o f)(x) means g(f(x))

Answer 3

basically, you start with g(x)

then you replace all copies of 'x' with f(x)

Answer 4

not quite following :(

Answer 5

so for example, say f(x) = 3x+1 g(x) = 2x

g(f(x)) means

g(x) = 2x

g(f(x)) = 2*f(x)

g(f(x)) = 2(3x+1)

Answer 6

ohh i see now :)

Answer 7

so for this equation, we need to solve for f(x) first right?

Answer 8

for this question, you simply use the steps I did above but for the given functions f(x) and g(x)

so for example, in choice D

\[\Large g(x) = \frac{x}{x+1}\]

\[\Large g(f(x)) = \frac{f(x)}{f(x)+1}\]

\[\Large g(f(x)) = \frac{x}{x+1}\]

which is NOT what we want, so choice D is out