Find each of the following functions and state their domains. (Enter the domains in interval notation.) f(x) = 4x + 7, g(x) = x2 + x

Question

(a) f o g

Domain=

(b) g o f

Domain=

(c) f o f

Domain=

(d) g o g

Domain=

Answer 1

Hi Schanda,

Thanks for posting your question here. As these are function compositions involving only polynomials, the domain of the resultant functions would always be all real numbers, or (-∞,∞). But let's see how:

(I'm assuming your second function g(x) is x^2+x).

fog = 4(x^2+x) + 7 = 4x^2 + 4x + 7 domain is all real numbers because there's no value of x that'll make it undefined.

gof = (4x+7)^2 + x = 16x^2 + 57x + 49 domain is all real numbers for same above reason

fof = 4(4x+7)+7 = 16x + 35 all real numbers above reason

gog = (x^2+x)^2 + x^2 + x = x^4 + 2x^3 + 2x^2 + x all real numbers above reason

For all of these you can state the domain, which is same for all, as (-∞,∞)

Hope it helped!

Best,

Tomaj

Answer 2