Question

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

Answer 1

( 1, ∞)  is the domain of (b o a)(x)

What is Function?

A function is defined as a relation between a set of inputs having one output each.

According to the question,

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

To find the domain of the composite function,

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

Therefore,

$3x - 3 \geq 0\\3x \geq 3\\x \geq 1$

Hence , [ 1, ∞ ] is is the domain of (b o a)(x).

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