Answered

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Given: g(x) = Square Root x - 4 and h(x) = 2x-8 What are the restrictions on the domain of g ⋅ h? x ≥ ____

Sagot :

Answer: [tex]x\geq 6[/tex]

Step-by-step explanation:

Given

[tex]g(x)=\sqrt{x-4}\\h(x)=2x-8[/tex]

Now, g of h i.e. [tex]g(h(x))[/tex]

Put h(x) in place of x in g(x)

[tex]\Rightarrow g(h(x))=\sqrt{(2x-8)-4}\\\\\Rightarrow g(h(x))=\sqrt{2x-12}[/tex]

Now, the value inside square root must be greater than zero

[tex]\Rightarrow 2x-12\geq 0\\\\\Rightarrow 2x\geq 12\\\\\Rightarrow x\geq 6[/tex]

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