Question

Only got two days this is last resort wouldn’t mind help

Answer 1

The product of the two functions √(3x) and √(48x) is computed by multiplying them to get √(144x^2), which simplifies to 12x. Therefore, the correct answer is C. (f · g)(x) = 12x.

The problem is to find the product of two functions f(x) and g(x), which are defined as f(x) = √(3x) and g(x) = √(48x) respectively. To solve for (f · g)(x), we must multiply the two functions together:

(f · g)(x) = f(x) · g(x) = √(3x) · √(48x) = √(3 · 48 · x · x) = √(144x^2).

Now, we notice that 144 is a perfect square, so taking the square root of 144x^2 gives us the final answer:

(f · g)(x) = 12x

Therefore, the correct choice is C. (f · g)(x) = 12x.

The probable question may be:

f(x)=\sqrt{3x}

g(x)=\sqrt{48x}

Find (f \cdot g)(x). Assume x>=0.

A. (f \cdot g)(x) = \sqrt{51x}

B. (f \cdot g)(x) = 12 \sqrt{x}

C. (f \cdot g)(x) = 12x

D. (f \cdot g)(x) = 9x

Answer 2

Option C.

Explanation:

If we have two functions:

f(x) and g(x)

the product is given by:

(f*g)(x) = f(x)*g(x)

So, if here we have

f(x) = √(3*x)

g(x) = √(48*x)

And remembering that the square root is distributive, so:

√a*√b = √(a*b)

We can write:

(f*g)(x) = f(x)*g(x) = √(3*x)*√(48*x) = √(3*x*48*x)

= √(3*48*x*x) = √(144*x^2) = √(144)*√(x^2)

And here we can use that:

12*12 = 144, then √144 = 12

and

x*x = x^2, then √x^2 = x

So:

√(144)*√(x^2) = 12*x

Then the correct option is C.