Given functions:
[tex]f(x)=2x^2-1[/tex][tex]g(x)=-5x[/tex]
The problem is asking for a multiplication of the functions, which can be done as follows:
[tex](fg)(x)=f(x)\times g(x)[/tex]
Then, we have to multiply the functions:
[tex](fg)(x)=(2x^2-1)\times(-5x)[/tex]
Simplifying we get:
[tex](fg)(x)=(2x^2\cdot-5x)-(1\cdot-5x)[/tex][tex](fg)(x)=-10x^3+5x[/tex]
In the second question, the problem is asking for a composition, which is equal to the following:
[tex](g\circ f)(x)=g(f(x))[/tex]
Then, in this case, we have to replace all the x in g(x) function by f(x):
[tex](g\circ f)(x)=-5\cdot(2x^2-1)[/tex]
Simplifying:
[tex](g\circ f)(x)=-10x^2+5[/tex]
Answer:
[tex](fg)(x)=-10x^3+5x[/tex][tex](g\circ f)(x)=-10x^2+5[/tex]
