T #b): Similar argumentation as described at #a).
I don't understand the writing of the term at #a). Do you mean:Find out the maximum on |R of the following functions :
a- h: x--> (1/|x|+3) +1.
b- K: x--> (2/1+x²) - 3.
To #b): The maximum of the complete term occurs when the fraction has it's maximum. Since the numerator is a constant the maximum is reached if the denominator has it's minimum. Since x² is positiv or zero the minimum of the denominator is obvious.