Composite Functions with a function with two ranges

Please help me with this problem!! Thank you in advance!!

[James Tursa]

This does not appear to be a MATLAB question. You simply need to plug the results of one function into the other function and simplify to get the requested expressions.

[Sadman Samin Khan]

But g(x) has two different functions with two different ranges. What to do about that??

Answer 1

[James Tursa]

For example, take the first one:

(g o f)(x)

This is just g(f(x)) which is g(x^2)

Assuming we are talking only about real inputs, x^2 is always non-negative. And when the input to g( ) is non-negative, the result is 3 times the input. So when you plug in x^2 to g( ) you simply need to multiply it by 3 to get the output. So the output is 3 times x^2.

Do the same analyses for the other parts of the assignment. You will need to consider each part of g( ) separately.