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vlada-n [284]
3 years ago
11

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

Mathematics
2 answers:
kondor19780726 [428]3 years ago
5 0
A(x) = 3x + 1
b(x) = √(x-4)

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

Answer: [1,∞]
tresset_1 [31]3 years ago
4 0

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

Explanation:

It is given that,

a(x)=3x+1

b(x)=\sqrt{x-4}

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

(b\circ a)(x)=b(a(x))

(b\circ a)(x)=b(3x+1)

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

(b\circ a)(x)=\sqrt{3x-3}

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

3x-3\geq 0

3x\geq 3

x\geq 1

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

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