Question

Consider the following functions.


`f(x)=x+3` and
`g(x)=(x+5)/(3)`
Step 2 of 2: Find the formula for (g∘f)(x) and simplify your answer. Then find the domain for (g∘f)(x). Round your answer to two decimal places, if necessary.

Answer 1

To find the formula for (g∘f)(x), we need to first evaluate g(f(x)):

g(f(x)) = g(x+3) = (3(x+3)+5)/3 = (3x+14)/3

So, (g∘f)(x) = (3x+14)/3

To find the domain for (g∘f)(x), we need to consider any restrictions on x that would make the function undefined. The only possible restriction is if the denominator of (3x+14)/3 is zero, which occurs when 3x+14=0. Solving for x, we get x=-14/3. Therefore, the domain of (g∘f)(x) is all real numbers except -14/3, or (-∞, -14/3) U (-14/3, ∞).