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Let f(x) = -2x + 7 and g(x) = -6x + 3. Find f.g and state its domain.Let f(x) = -2x + 7 and g(x) = -6x + 3. Find and state its domain.-14x2 + 36x - 18; all real numbers12x2 - 48x + 21; all real numbers-14x2 + 36x - 18; all real numbers except x = 712x2 - 48x + 21; all real numbers except x = 1

Respuesta :

Explanation:

We are given two functions:

[tex]\begin{gathered} f(x)=-2x+7 \\ g(x)=-6x+3 \end{gathered}[/tex]

The question wants us to obtain f.g and its's domain

To do so,

Let us first obtain f.g

[tex]fg=f(x)\times g(x)=\mleft(-2x+7\mright)\times(-6x+3)=12x^2-48x+21[/tex]

Next, we will find its domain

We can use the graph below to help

The domain of f.g is

[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: -\infty\: Therefore[tex]\text{The domain is all real numbers}[/tex]

Hence

The answer is the second option

[tex]12x^2-48x+21;\text{ All real numbers}[/tex]

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