Mathematics: If f(x)= sqrtx-3 and g(x)=1-x^2, then what do you notice about the domain of (fxg)(x)?

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If f(x)= sqrtx-3 and g(x)=1-x^2, then what do you - id3123011548, lilymoniquesalaiz

temoshojayne

05.01.2022

$x\geq0$ if $f(x)=\sqrt{x}-3$

$x\geq3$ if $f(x)=\sqrt{x-3}$

Step-by-step explanation:

If $f(x)=\sqrt{x}-3$ then the domain of f(x) is all positive real numbers. This is $x\geq0$

On the other hand the domain of g(x) would be all real numbers because it is a polynomial function

Therefore

$(f*g)(x) = f(x)*g(x)\\\\(f*g)(x) =(\sqrt{x}-3)*(1-x^2)$

$(f*g)(x) =\sqrt{x}-x^2(\sqrt{x})-3+3x^2$

Then the domain of f(x) *g(x) will be the same domain of f(x)

All positive real numbers, $x\geq0$ or x ∈ [0, ∞)

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If f(x) = $\sqrt{x-3}$ then the domain of f(x) is

$x-3\geq0\\\\x\geq3$

Therefore

$(f*g)(x) = f(x)*g(x)\\\\(f*g)(x) =(\sqrt{x-3})*(1-x^2)$

$(f*g)(x) =\sqrt{x-3}-x^2(\sqrt{x-3})$

Then the domain of f(x) *g(x) will be the same domain of f(x)

$x\geq3$ or x ∈ [3, ∞)

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