If a(x) = 3x + 1 and b(x)= √x-4 , what is the domain of (b*a)(x)

a(x) = 3x + 1
b(x) = √(x-4)

Therefore
[tex](b \circ a) (x) = \sqrt{3x+1-4} =\sqrt{3x-3} [/tex]
This composition of functions is only defined as a real number when x≥0.
Therefore its domain is x = [1,∞]

Answer: [1,∞]

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DelcieRiveria DelcieRiveria · Answer 2 · 2018-11-16T09:00:58+01:00

Answer: The correct option is C. The domain of [tex](b\circ a)(x)[/tex] is [tex][0,\infty)[/tex].

Explanation:

It is given that,

[tex]a(x)=3x+1[/tex]

[tex]b(x)=\sqrt{x-4}[/tex]

First we have to find the composite function [tex](b\circ a)(x)[/tex].

[tex](b\circ a)(x)=b(a(x))[/tex]

[tex](b\circ a)(x)=b(3x+1)[/tex]

[tex](b\circ a)(x)=\sqrt{3x+1-4}[/tex]

[tex](b\circ a)(x)=\sqrt{3x-3}[/tex]

We know that a root function is defined for only positive values therefore the composite function is defined if,

[tex]3x-3\geq 0[/tex]

[tex]3x\geq 3[/tex]

[tex]x\geq 1[/tex]

The function is defined for all the values of x which are greater than or equal to 1. Therefore the domain of [tex](b\circ a)(x)[/tex] is [tex][0,\infty)[/tex] and option C is correct.