If f(x)=2x=√+2x and g(x)=√2⋅x , evaluate (f⋅g)(x) when x=2 .

Answer 1

First, let's simplify f(x):

f(x) = 2x + √(2x)

Now let's simplify g(x):

g(x) = √2 * x

To find (f⋅g)(x), we need to multiply f(x) and g(x).

(f⋅g)(x) = f(x) * g(x)

= (2x + √(2x)) * (√2 * x)

= (2x) * (√2 * x) + (√(2x) * √2 * x)

= 2√2 * x^2 + 2x^2

Now let's substitute x=2 into (f⋅g)(x):

(f⋅g)(2) = 2√2 * (2)^2 + 2(2)^2

= 2√2 * 4 + 2 * 4

= 8√2 + 8

Therefore, when x=2, (f⋅g)(x) is equal to 8√2 + 8.

Answer 2

is this correct?

Answer 3

Apologies for the mistake in my response. It looks like there was a confusion in the initial function f(x).

The corrected equation for f(x) should be:
f(x) = 2x + √(2x)

The equation for g(x) remains the same:
g(x) = √2 * x

Now let's evaluate (f⋅g)(x) when x = 2:

f(2) = 2(2) + √(2(2))
= 4 + √(4)
= 4 + 2
= 6

g(2) = √2 * 2
= 2√2

To find (f⋅g)(x), we multiply f(x) and g(x):

(f⋅g)(x) = f(x) * g(x)
= [2x + √(2x)] * [√2 * x]
= (2x * √2 * x) + (√(2x) * √2 * x)
= 2√2 * x^2 + 2x^2

Substituting x = 2 into (f⋅g)(x):

(f⋅g)(2) = 2√2 * (2)^2 + 2(2)^2
= 2√2 * 4 + 2 * 4
= 8√2 + 8

Therefore, when x = 2, the value of (f⋅g)(x) is 8√2 + 8.