Given that f(x) = −x + 4 and g(x) = −2x − 3, solve for f(g(x)) when x = 2.

Hello : 
f(x) = −x + 4 and g(x) = −2x − 3,
 solve for f(g(x)) when x = 2.
f(g(2)) = f(-7)
 because : g(2) = -2(2)-3 = -7
f(g(2)) = -(-7)+4 =11

11

Step-by-step explanation:

g(2)=-7

f(-7)=11

D

Step-by-step explanation:

First you need to find which function represents f(g(x)) and then you replace each x in this new function by 2.

f(4), for example, is f when x = 4, right? So f(4) = -4+4 = 0

So, f(g(x)) will represent f when x = g(x). x = g(x) when x = -2x-3

So, f(g(x)) = f(-2x-3) = -(-2x-3) + 4

                               = -(-2x)-(-3)+4

                              = 2x + 3 + 4

                              = 2x + 7

So f(g(x)) = 2x + 7.

Now when x = 2, f(g(x)) = 2*2 + 4 = 11, which is option D.

f(g(x))= 11

Step-by-step explanation:

This question asks us to find f(g(x)) when x=2. Therefore, we can substitute 2 in for x.

f(g(x)), x=2

f(g(2))

First, we must find g(2).

We know that g(x)= -2x-3. We can plug 2 in for each x and solve.

g(x)= -2x -3, x=2

g(2)= -2(2)-3

First, multiply -2 and 2.

g(2)= -4-3

Then, subtract 3 from -4.

g(2)= -7

Let's return to our function: f(g(2)). We know that g(2)= -7. Thus, we can substitute -7 in for g(2).

f(g(2)), g(2)= -7

f(-7)

Now we must find f(-7). We know that f(x)= -x+4. We can plug -7 in for x and solve.

f(x)= -x+4 , x= -7

f(-7)= -(-7) +4

f(-7)= 7+4

Add 7 and 4

f(-7)= 11

Our final answer is: f(g(x))= 11

F(x) = -x + 4
g(x) = -2x - 3

f(g(x)) = -(-2x - 3) + 4 = 2x + 3 + 4 = 2x + 7
f(g(2)) = 2(2) + 7 = 4 + 7 = 11

f(x)= -x+4 and g(x) =-2x-3 

f(g(x))= -(-2x-3) + 4= 2x +3+4 =2x + 7

Answer is f(g(x)) =2x+7

G(2) = -4-3 = -7 

So f(g(2)) = f(-7) = 7+4 = 11

Input
f(g(x))=-(g(x))+4=
g(x)=-2x-3
so
if x=2
f(g(2))=-(g(2))+4
g(2)=-2(2)-3=-4-3=-7

f(g(2))=-(-7)+4=7+4=11

f(g(2))=11