If the function f defined by f(x)= array llc x, & if & x 0 3 x+ , & if & 0 4 array . where, and are real constants, is continuous on R , then ^2+ ^2=

Step-by-step solution

f(x) is continuous on R , so array rlrl at x=0, & _ x 0⁺ f(x) & =f(0) & 0+ = 0 & =1 & =1 at x=2, & _ x 2⁻ f(x) & =f(2) 6+ & =2 +3 array aligned 7 & =2 +3 2 & =4 =2 So, ^2+ ^2 & =1+4=5 . aligned