Question

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

Answer 1

Answer:

C. (1,infinity)

Step-by-step explanation:

Answer 2

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,

$[1, \infty ]$