consider the equations f(x)

Question

Could anyone please help me out with this.

 

consider the equations f(x)= -6x-1 and g(x)= 4x^2 select the solution for (fg)(x)

 

a- -6x-1+4x^2

b- -24x^3-4x^3

c- -24x^2-1

d- -24x^5

Answer 1

(fg)(x) is really (f o g)(x) or f(g(x)), which is the composition of the two functions. When composing two functions you are substituting in the value of the second function into the formula of the first function. So for f(x) and g(x), the g(x) now represents the value of x in the function f(x). Creating f(g(x)).  

 

Given f(x) = -6x - 1 and g(x) = 4x², then f(g(x)) = (-6(g(x)) - 1).

 

Replace the g(x) with it value 4x²; then f(g(x)) = -6(4x²) - 1 = -24x² - 1

 

 

So (fg)(x) = -24x² - 1, which is choice C. 

 

 

Please note: usually (fg)(x) ≠ (gf)(x)  It is not commutative.