Domain and Range

Having problems with the following:

f(x) = 3x g(x) = x3 - 1 NOTE x3 should be squared

(f o g)(x) = f(x3-1) = 3x(x3-1)

(g o f)(x) = g(3x) = 1(3x)3

f(f(x)) = f(3x) - 3x

(f .f)(x) = (3x) . (3x)



f(x) = 1/x3 g(x) = 4x + 1 NOTE x3 should be squared

(f o g)(x) f(4x + 1) =

(g o f)(x)

f(f(x))

(f .f)(x)


I am not sure what I am doing?

Thanks,

Queenie





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I'll help you on the first one.

f(x) = 3x
g(x) = x^3 - 1

function composition: f(g(x)) is actually equal to 3(x^3 - 1) because for all values x in f(x), f(x) = 3x.... so, f(g(x)) = 3(x^3 - 1)

Now what is the domain (input) of 3(x^3 - 1) ? are you allowed to put in all real numbers?

Now for the range (output) of 3(x^3 - 1) can you get out all real numbers?