Given gs 3ssquared 1s find the following g1 g1 g2 gx gsh

Given g(s) = 3s(squared) + 1/s , find the following.

g(1)

g(-1)

g(2)

g(x)

g(s+h)

g(s+h) - g(s)

Solution

given g(s) = 3s²+ (1/s)

g(1)= 3*1²+ (1/1)=3+1=4

g(-1)= 3*(-1)²+ (1/(-1))=3-1=2

g(2)= 3*2²+ (1/2)=12+(1/2)=25/2

g(x)= 3x²+ (1/x)

g(s+h)=3(s+h)²+ (1/(s+h)) =3s²+6sh+3h² + (1/(s+h))

g(s+h) - g(s) =3s²+6sh+3h² + (1/(s+h)) -3s²- (1/s)

g(s+h) - g(s) =6sh+3h² + (1/(s+h)) - (1/s)

g(s+h) - g(s) =6sh+3h² + ((s-s-h)/(s(s+h)))

g(s+h) - g(s) =6sh+3h² - (h/(s(s+h)))