Answer:
[tex]x\geq0[/tex] if [tex]f(x)=\sqrt{x}-3[/tex]
[tex]x\geq3[/tex] if [tex]f(x)=\sqrt{x-3}[/tex]
Step-by-step explanation:
If [tex]f(x)=\sqrt{x}-3[/tex] then the domain of f(x) is all positive real numbers. This is [tex]x\geq0[/tex]
On the other hand the domain of g(x) would be all real numbers because it is a polynomial function
Therefore
[tex](f*g)(x) = f(x)*g(x)\\\\(f*g)(x) =(\sqrt{x}-3)*(1-x^2)[/tex]
[tex](f*g)(x) =\sqrt{x}-x^2(\sqrt{x})-3+3x^2[/tex]
Then the domain of [tex]f(x) *g(x)[/tex] will be the same domain of [tex]f(x)[/tex]
All positive real numbers, [tex]x\geq0[/tex] or x ∈ [0, ∞)
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If f(x) = [tex]\sqrt{x-3}[/tex] then the domain of f(x) is
[tex]x-3\geq0\\\\x\geq3[/tex]
Therefore
[tex](f*g)(x) = f(x)*g(x)\\\\(f*g)(x) =(\sqrt{x-3})*(1-x^2)[/tex]
[tex](f*g)(x) =\sqrt{x-3}-x^2(\sqrt{x-3})[/tex]
Then the domain of [tex]f(x) *g(x)[/tex] will be the same domain of [tex]f(x)[/tex]
[tex]x\geq3[/tex] or x ∈ [3, ∞)
Answer:
The domain of f, and thus the range of g, is restricted to values greater than or equal to 3.
If 1 minus x squared is greater than or equal to 3, then x squared must be less than –2.
Since x squared cannot be less than a negative number, the function is undefined for all values of x.
Step-by-step explanation:
