Question

If a(x) = 3x + 1 and mc017-1.jpg, what is the domain of mc017-2.jpg?
mc017-3.jpg
mc017-4.jpg
mc017-5.jpg
mc017-6.jpg

Answer 1

I can’t see the linked image files (mc017-1.jpg etc.). Could you either paste the function(s) here as text or upload the images? I’ll need the inner function shown in those images to find the domain.

If you want to proceed on your own, here’s the general rule and how to apply it:

- a(x) = 3x + 1 has domain all real numbers.
- If you are asked for the domain of a(h(x)) (the composition a∘h), the domain is:
{ x in domain(h) such that h(x) is in domain(a) }.
- Since domain(a) = all reals, the domain of a(h(x)) is simply the domain of h(x).
- So you only need to find the domain restrictions coming from h(x): exclude x that make denominators 0, make even-indexed radicals have negative radicands, or produce other undefined expressions (logarithms require positive arguments, etc.).

Examples:
- If h(x) = (x+2)/(x-3), domain is x ≠ 3.
- If h(x) = sqrt(x-5), domain is x ≥ 5.
- If h(x) = ln(x+1), domain is x > −1.

Send the inner-function expression (or re-upload the images) and I’ll compute the exact domain.