Question

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

answers choices are:
-infinity, infinity
0, infinity
1, infinity
4, infinity

Answer 1

`[1, \infty ]`

Step-by-step explanation

The given functions are:

`a(x) = 3x + 1`

`b(x) = √(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) = √(3x + 1 - 4)`

This simplifies to,

`(b \circ \: a)(x) = √(3x - 3)`

This function is defined for

`3x - 3 \geqslant 0`

`3x \geqslant 3`

`x \geqslant 1`

This can be rewritten as,

`[1, \infty ]`