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Let f(x)= √x+1/3 and g(x)= √x. Find (f * g)(x). Assume all appropriate restrictions to the domain.

A. (f * g)(x)= √x^2+x / 3

B. (f * g)(x)= x+1 / 3

C. (f * g)(x)= x^2+x / 3

D. (f * g)(x)= x+√x / 3

Respuesta :

carlosego

For this case we have the following functions:

[tex]f (x) = \sqrt {x} + \frac {1} {3}\\g (x) = \sqrt {x}[/tex]

We must find[tex](f * g) (x)[/tex]. By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex](f * g) (x) = (\sqrt {x} + \frac {1} {3}) * \sqrt {x}\\(f * g) (x) = (\sqrt {x}) ^ 2+ \frac {1} {3} (\sqrt {x})\\(f * g) (x) = x + \frac {\sqrt {x}} {3}[/tex]

Answer:

Option D

profantoniofonte

Answer:

D

Step-by-step explanation:

Operating with functions f(x) and g(x).

One of the operations is the product: f(x) *g(x) = (fg)(x)

So let's calculate the product of these two functions. The Domain under the radicals must be x

[tex]The \:values\: of \:the\: Domain\: must\: be \:x\geq 0\\\\f(x)=\sqrt{x} +\frac{1}{3} \:and\:g(x)=\sqrt{x} \\(f*g)(x)=(\sqrt{x} +\frac{1}{3} )(\sqrt{x})=\\(fg)(x)=\sqrt{x^{2} } +\frac{\sqrt{x} }{3} \\(fg)(x)=x+\frac{\sqrt{x} }{3}[/tex]

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