Answer :
To evaluate the product of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], let's start by expressing both functions clearly:
[tex]\( f(x) = 3x^3 - 5x \)[/tex]
[tex]\( g(x) = 3x^4 \)[/tex]
To find [tex]\( f(x) \cdot g(x) \)[/tex], multiply them together:
[tex]\[ f(x) \cdot g(x) = (3x^3 - 5x) \cdot (3x^4) \][/tex]
We will distribute [tex]\( 3x^4 \)[/tex] across the terms in [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) \cdot g(x) = 3x^3 \cdot 3x^4 - 5x \cdot 3x^4 \][/tex]
Now, perform the multiplications:
[tex]\[ 3x^3 \cdot 3x^4 = 9x^{3+4} = 9x^7 \][/tex]
[tex]\[ -5x \cdot 3x^4 = -15x^{1+4} = -15x^5 \][/tex]
Putting it all together, we get:
[tex]\[ f(x) \cdot g(x) = 9x^7 - 15x^5 \][/tex]
Therefore, the correct answer is:
(B) [tex]\( f(x) \cdot g(x) = 9x^7 - 15x^5 \)[/tex]
[tex]\( f(x) = 3x^3 - 5x \)[/tex]
[tex]\( g(x) = 3x^4 \)[/tex]
To find [tex]\( f(x) \cdot g(x) \)[/tex], multiply them together:
[tex]\[ f(x) \cdot g(x) = (3x^3 - 5x) \cdot (3x^4) \][/tex]
We will distribute [tex]\( 3x^4 \)[/tex] across the terms in [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) \cdot g(x) = 3x^3 \cdot 3x^4 - 5x \cdot 3x^4 \][/tex]
Now, perform the multiplications:
[tex]\[ 3x^3 \cdot 3x^4 = 9x^{3+4} = 9x^7 \][/tex]
[tex]\[ -5x \cdot 3x^4 = -15x^{1+4} = -15x^5 \][/tex]
Putting it all together, we get:
[tex]\[ f(x) \cdot g(x) = 9x^7 - 15x^5 \][/tex]
Therefore, the correct answer is:
(B) [tex]\( f(x) \cdot g(x) = 9x^7 - 15x^5 \)[/tex]
