Answer:
[tex](fg)(x)=4x^3+12x^2-5x-15[/tex]
First option is correct.
Step-by-step explanation:
We have been given that
[tex]f(x)=4x^2-5[/tex]
[tex]g(x)=x+3[/tex]
We know that [tex](fg)(x)=f(x)g(x)[/tex]
Hence, we have to find the product of f(x) and g(x)
[tex](fg)(x)=(4x^2-5)(x+3)[/tex]
Apply distributive property
[tex](fg)(x)=4x^2\cdot x+4x^2\cdot3-5x-5\cdot3[/tex]
Simplifying, we get
[tex](fg)(x)=4x^3+12x^2-5x-15[/tex]
First option is correct.
