Given that f(x) = −x + 4 and g(x) = −2x − 3, solve for f(g(x)) when x = 2. (1 point)
(a) −14
(b) −7
(c) 7
(d) 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.

cosine

step-by-step explanation:

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)