Let’s say that I want this function to be continuous and for this I have to discover certain values to a and b. How do I put this in Wolfram|Alpha?
The function will be continuous if the piecewise components are equal at their boundaries.
Thus you want to solve the following system:
a (0)+2 b = (0)^2 +3 a - b
(2)^2+3a-b = 3 (2) -5
You could input this as Solve[{a0+2 b = 0^2 +3 a - b, 2^2+3a-b = 32 -5},{a,b}]
Though this shouldn’t require Wolfram’s help, as you can simplify the system pretty easily!
a (0)+2 b = 2b
(0)^2 +3 a - b= 3a-b
2b= 3a-b \Longrightarrow b=a
(2)^2+3a-b = 4 +3 a-b= 4+2 a
3 (2) -5 = 6-5 = 1
4+2a = 1 \Longrightarrow 2a = -3 \Longrightarrow a =-3/2 =b