Answer
$$\eqalign{
& g\left( {x,y,z} \right) = {e^{x + y + z}} \cr
& \cr
& \left( a \right){\text{ Find }}g\left( {0,0,0} \right) \cr
& g\left( {0,0,0} \right) = {e^{0 + 0 + 0}} \cr
& g\left( {0,0,0} \right) = 1 \cr
& \cr
& \left( b \right){\text{ Find }}g\left( {1,0,0} \right) \cr
& g\left( {1,0,0} \right) = {e^{1 + 0 + 0}} \cr
& g\left( {1,0,0} \right) = e \cr
& \cr
& \left( c \right){\text{ Find }}g\left( {0,1,0} \right) \cr
& g\left( {0,1,0} \right) = {e^{0 + 1 + 0}} \cr
& g\left( {0,1,0} \right) = e \cr
& \cr
& \left( d \right){\text{ Find }}g\left( {z,x,y} \right) \cr
& g\left( {z,x,y} \right) = {e^{z + x + y}} \cr
& \cr
& \left( e \right){\text{ Find }}g\left( {x + h,y + k,z + l} \right) \cr
& g\left( {x + h,y + k,z + l} \right) = {e^{x + h + y + k + z + l}} \cr} $$
Work Step by Step
$$\eqalign{
& \left( a \right)1 \cr
& \left( b \right)e \cr
& \left( c \right)e \cr
& \left( d \right){e^{z + x + y}} \cr
& \left( e \right){e^{x + h + y + k + z + l}} \cr} $$
