If fx x2 x and gx 3x evaluate and simplify fa h fa h a

If f(x) = x² + x and g(x) = 3/x , evaluate and simplify

f(a + h) f(a)

------------------

h

and

g(a + h) g(a)

----------------------

h

when a = 1, a = 2, a = 1, a = x

Solution

Solution : ((a+h)^2+(a+h)-a^2-a)/h

=(a^2+2ah+h^2+a+h- a^2-a)/h

=(2ah+h^2+h)/h

=2a+h+1.

For a=1,

= 2+h+1

=3+h.

For a= 2,

Thus 2(2)+h-1

=5+h.

And for a=-1.

=2(-1)+h+1

=h-1.

a=x

=2(x)+h+1.

Now (g(a+h)-g(a))/h = (3/(a+h)-3/a)/h

=(3a-3a-3h)/h

=-3.

For a =1,2,-1, and x

=-3.