QuestionJune 17, 2025

If a(x)=3x+1 and b(x)=sqrt (x-4) what is the domain of (bcirc a)(x) (-infty ,infty ) [0,infty ) [1,infty ) [4,infty )

If a(x)=3x+1 and b(x)=sqrt (x-4) what is the domain of (bcirc a)(x) (-infty ,infty ) [0,infty ) [1,infty ) [4,infty )
If a(x)=3x+1 and b(x)=sqrt (x-4) what is the domain of (bcirc a)(x)
(-infty ,infty )
[0,infty )
[1,infty )
[4,infty )

Solution
4.4(233 votes)

Answer

\( [1, \infty) \) Explanation 1. Determine the domain of ( a(x) ) The function ( a(x) = 3x + 1 ) is a linear function, so its domain is \( (-\infty, \infty) \). 2. Determine the domain of ( b(x) ) The function \( b(x) = \sqrt{x - 4} \) requires \( x - 4 \geq 0 \). Thus, \( x \geq 4 \), so the domain is \( [4, \infty) \). 3. Find the domain of ( (b \circ a)(x) ) For \( (b \circ a)(x) = b(a(x)) = \sqrt{3x + 1 - 4} = \sqrt{3x - 3} \), we need \( 3x - 3 \geq 0 \). Solving gives \( x \geq 1 \).

Explanation

1. Determine the domain of ( a(x) )<br /> The function ( a(x) = 3x + 1 ) is a linear function, so its domain is \( (-\infty, \infty) \).<br />2. Determine the domain of ( b(x) )<br /> The function \( b(x) = \sqrt{x - 4} \) requires \( x - 4 \geq 0 \). Thus, \( x \geq 4 \), so the domain is \( [4, \infty) \).<br />3. Find the domain of ( (b \circ a)(x) )<br /> For \( (b \circ a)(x) = b(a(x)) = \sqrt{3x + 1 - 4} = \sqrt{3x - 3} \), we need \( 3x - 3 \geq 0 \). Solving gives \( x \geq 1 \).
Click to rate:

Similar Questions