Let f(x) = x - 3 and g(x) = 2x + 4. What is f(g(x)) ?

Question

Choose one answer.
A. 2x + 7
 

B. 2x - 2
 

C. 2x + 1
 

D. 3x + 1

Answer 1

May,

 

f(g(x)) = g(x) -3

 

           = 2x + 4 -3

 

           = 2x + 1

Answer 2

This is a function composition. f(g(x)) means that for each x, we evaluate g at x, i.e. plug x into g. We then take the output and plug it into f.

 

We'll start by writing down the formula for f in terms of x:

 

x -3

 

Now, everywhere you see an x, replace it with the formula for g in x: (g(x) = 2x+4. We get

 

f(g(x)) = g(x)-3

           = (2x+4)-3

 

Now simplify to get

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

 

which is C.