Question

If a(x) = 3x + 1 and b(x) = (x-4) what is the domain of (boa)(x)?

a) ([infinity],0)
b) [ -[infinity],[infinity]]
c) [1, [infinity])
d) [4,[infinity] )

Answer 1

To find the domain of (boa)(x), we need to determine the valid values of x for which the function is defined. Given that b(x) = (x-4) and a(x) = 3x + 1, the domain of (boa)(x) is (-∞, ∞).

Step-by-step explanation:

To find the domain of (boa)(x), we need to determine the valid values of x for which the function is defined. The function (boa)(x) is the composition of the functions b(x) and a(x), which means we need to find the domain of b(x) first. Given that b(x) = (x-4), there are no restrictions on the values of x, so the domain of b(x) is (-∞, ∞).

Next, we need to determine the domain of a(x). The function a(x) = 3x + 1 is defined for all real values of x since there are no restrictions or divisions by zero involved.

Finally, we can find the domain of (boa)(x) by considering the restrictions from both b(x) and a(x). Since b(x) has no restrictions and a(x) is defined for all real numbers, the domain of (boa)(x) is also (-∞, ∞).