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leonid [27]
3 years ago
15

If a(x)=3x+1 and b(x)=square root x-4, what is the domain of (b o a)(x)?

Mathematics
2 answers:
Dennis_Churaev [7]3 years ago
4 0

Answer:

C. (1,infinity)

Step-by-step explanation:

Bond [772]3 years ago
3 0

ANSWER

[1, \infty ]

EXPLANATION

The given functions are:

a(x) = 3x + 1

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

We want to find the domain of the composite function;

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

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

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

This simplifies to,

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

This function is defined for

3x - 3 \geqslant 0

3x \geqslant 3

x \geqslant 1

This can be rewritten as,

[1, \infty ]

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