For the Given Functions F and G, Find the Requested $f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$

question 76

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$
Find $f \cdot g$ .

• A) \(( f \cdot g ) ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 6\); all real numbers
• B) \(( f \cdot g ) ( x ) = 25 x ^ { 6 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6\); all real numbers
• C) \(( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6\); all real numbers
• D) \(( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6 ; \{ x \mid x \neq 0 \}\)

---

Definitions:

Discount Rate

The interest rate used to determine the present value of future cash flows in discounted cash flow analysis.

Net Present Value

A financial metric that calculates the present value of expected future cash flows relative to the initial investment, used to assess the profitability of an investment.

Investment Project

An undertaking requiring capital investments with the aim of generating future returns.

Interest Rate

is the percentage of a loan amount charged by the lender to the borrower for the use of assets.