Question

Given f (x) = 3x – 7 and g (x) = 2 – 3x. Find (f . g)(x)

a) 9x² −13x+14
b) 9x² −13x−14
c) −9x² +13x−14
d) −9x² +13x+14

Answer 1

To find (f . g)(x), we need to apply the composition of functions. Substituting g(x) = 2 - 3x into f(x) = 3x - 7, we get (f . g)(x) = f(2 - 3x). Evaluating (f . g)(x) gives us -9x - 1.

Step-by-step explanation:

To find (f . g)(x), we need to apply the composition of functions.

The composition of functions is given by (f . g)(x) = f(g(x)).

Substituting g(x) = 2 - 3x into f(x) = 3x - 7, we get (f . g)(x) = f(2 - 3x).

Now, let's evaluate (f . g)(x) by substituting 2 - 3x into the expression for f(x):

f(2 - 3x) = 3(2 - 3x) - 7 = 6 - 9x - 7 = -9x - 1.

Therefore, the answer is (d) -9x² + 13x + 14.