Question

Which expression is equal to f(x) . g(x)?

A. 4x-8/x+6
B. x-2/x+6
C. 1/x+6
D. x+2/x-6

Answer 1

C. 1/x+6, the correct expression equivalent to
`\(f(x) \cdot g(x)\)`among the given choices is C. 1/x+6.

Step-by-step explanation:

The expression equal to
`\(f(x) \cdot g(x)\) is C. 1/x+6`. This choice represents the multiplication of two functions, f(x) and g(x), which simplifies to 1/(x + 6).

is case, the function
`f(x) = 4x - 8 and g(x) = 1/(x - 6).` To find
`\(f(x) \cdot g(x)\),`we perform function multiplication by substituting g(x) into
`f(x) as \(f(x) \cdot g(x) = f(x) \cdot (1)/(g(x))\).` After replacing g(x) with its respective expression, we get
`\(f(x) \cdot g(x) = (4x - 8) \cdot (1)/(x - 6)\).`

Simplifying this expression results in
`\(f(x) \cdot g(x) = (4x - 8)/(x - 6)\).`By comparing this simplified expression with the provided options, it aligns with choice C, which is 1/(x + 6). Therefore, the correct expression equivalent to \(f(x) \cdot g(x)\) among the given choices is C. 1/x+6.