Question

f,g:R-------->R

determinati: f+g, f-g și f x g

a) și b)

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Answer 1

Răspuns:

a)

(f+g)(x) = f(x)+g(x) = $\left \{ {{2x-3+x-1, x\leq 0} \atop {2x-3+x+3, x>0}} \right. = \left \{ {{3x-4, x\leq 0} \atop {3x, x>0}} \right.$

(f-g)(x) = f(x)-g(x) = $\left \{ {{2x-3-x+1, x\leq 0} \atop {2x-3-x-3, x>0}} \right. = \left \{ {{x-2, x\leq 0} \atop {x-6, x>0}} \right.$

(f·g)(x) = f(x)·g(x) = $\left \{ {{(2x-3)(x-1), x\leq 0} \atop {(2x-3)(x+3), x>0}} \right. = \left \{ {{2x^{2}-2x-3x+3, x\leq 0} \atop {2x^{2}+6x-3x-9 , x>0}} \right. = \left \{ {{2x^{2}-5x-9, x\leq 0} \atop {2x^{2}+3x+9 , x>0}} \right.$

(f°g)(x) = f(g(x)) = $\left \{ {{2(x-1)-3, x\leq0 } \atop {2(x+3)-3,x>0}} \right. = \left \{ {{2x-5, x\leq0 } \atop {2x-3,x>0}} \right.$

b) vezi atasat