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If \(\displaystyle{f(x)=x^{(x+1)}(x+2)^{(x+3)}}\), then find the value of \(f(0)+f(-1)+f(-2)+f(-3)\).

 Oct 8, 2019
 #1
avatar+104962 
+2

f(0)  =  0^(0+1) * (0 + 2)^(0 + 3)  =  0^1  * 2^3  =   0

 

f(-1) =  (-1)^(-1 + 1) * (-1 + 2)^(-1 + 3)  = (-1)^0 * (1)^(2)  = 1 * 1  = 1

 

f(-2)  =  (-2)^(-2 + 1) * (-2 +2)^(-2 + 3)  =  (-2)^(-1)* (0)^(1)  =  0

 

f(-3)  =  (-3)^(-3 + 1) * (-3 + 2)^(-3 + 3)  = (-3)^(-2) * (-1)^0  =  (1/9)*(1)  = 1/9

 

The sum of these  =   1 1/9    =   10/9

 

 

cool cool cool

 Oct 9, 2019
 #2
avatar+1196 
+1

thanks mate

 Oct 9, 2019

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