Let ƒ(x) = 4x − 7 and g(x) = 5 + 9x. What are ƒ + g and ƒ − g? What are their domains?

We want to sum (and subtract) two functions and then find the domains. Remember that the domain of a function is the set of all the possible values of x that we can input in the function.

We have:

f(x) = 4x - 7

g(x) = 5 + 9x

The sum is just:

f(x) + g(x) = 4x - 7 + 5 + 9x = 13x - 2

And this is a linear function, so the domain (like in all linear functions) is the set of all real numbers.

For the difference we have:

f(x) - g(x) = (4x - 7) - (5 + 9x) = -5x - 12

Again, the domain is the set of all real numbers.

If you want to learn more, you can read:

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Step-by-step explanation:

f(x) + g(x) = 4x - 7 + 5 + 9x = 13x - 2

f(x) - g(x) = 4x - 7 - 5 - 9x = -5x - 12

all it means is function 3