Answer :
Option (c) is correct
[tex](fg)(x)=2x^3+8x^2-3x-12[/tex]
Step-by-step explanation:
Given : functions [tex]f(x)=2x^2-3[/tex] and [tex]g(x)=x+4[/tex]
We have to calculate (fg)(x) and choose the correct from the given options.
Consider (fg)(x) = (f • g)(x) = f(x) • g(x)
That is we have to multiply the two functions.
Consider the given functions [tex]f(x)=2x^2-3[/tex] and [tex]g(x)=x+4[/tex]
Then,
[tex]f(x)\cdot g(x) =(2x^2-3)(x+4)[/tex]
Multiply the each term of first bracket with each term of second bracket, we have,
[tex]f(x)\cdot g(x) =2x^2\cdot (x+4)-3\cdot(x+4)[/tex]
Simplify, we have,
[tex]f(x)\cdot g(x) =2x^3+8x^2-3x-12[/tex]
Thus, [tex](fg)(x)=2x^3+8x^2-3x-12[/tex]
Option (c) is correct.
