Use the functions below.

Question

f(x)=3⋅4x
g(x)=13⋅4x
What is (fg)(x)
? What is the domain of (fg)(x)
?

(1 point)
Responses

(fg)(x)=19
and the domain of (fg)(x)
is (−∞,∞)
.
open paren f over g close paren of x is equal to 1 ninth and the domain of open paren f over g close paren of x is open paren negative infinity comma infinity close paren .

(fg)(x)=9
and the domain of (fg)(x)
is (−∞,∞)
.
open paren f over g close paren of x is equal to 9 and the domain of open paren f over g close paren of x is open paren negative infinity comma infinity close paren .

(fg)(x)=9
and the domain of (fg)(x)
is x≥3
.
open paren f over g close paren of x is equal to 9 and the domain of open paren f over g close paren of x is x is greater than or equal to 3 .

(fg)(x)=19
and the domain of (fg)(x)
is x≥3
.
open paren f over g close paren of x is equal to 1 ninth and the domain of open paren f over g close paren of x is x is greater than or equal to 3 .
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Answer 1

To find \((fg)(x)\), we need to calculate the product of the functions \(f(x)\) and \(g(x)\):

1. \(f(x) = 3 \cdot 4^x\)
2. \(g(x) = 13 \cdot 4^x\)

Now, let's compute \((fg)(x)\):

\[ (fg)(x) = f(x) \cdot g(x) = (3 \cdot 4^x) \cdot (13 \cdot 4^x) \]

We can combine the constants and the exponential terms:

\[ (fg)(x) = 3 \cdot 13 \cdot (4^x \cdot 4^x) = 39 \cdot (4^x)^2 = 39 \cdot 4^{2x} \]

So, \((fg)(x) = 39 \cdot 4^{2x}\).

Next, we will determine the domain of \((fg)(x)\). Since both \(f(x)\) and \(g(x)\) are defined for all real numbers (as exponentials are defined for all \(x\)), the domain of \((fg)(x)\) is also:

\[ \text{Domain} = (-\infty, \infty) \]

So, the answer is:

\((fg)(x) = 39 \cdot 4^{2x}\) and the domain of \((fg)(x)\) is \((-∞, ∞)\).

None of the provided responses match this. If a more specific answer format is required, please clarify!