please solve Let fx x12 and x a 0 Then fx fax a x12 a

please solve

Let f(x) = x^-1/2 and x > a > 0. Then f(x) - f(a)/x - a = x^1/2 - a^1/2. = -1/squareroot xa(squareroot a + squareroot x). = x^-1/2 - a^-1/2.

Solution

given f(x)=x^-1/2=>f(x)=1/x

(f(x)-f(a))/(x-a)

=((1/x)-(1/a))/(x-a)

=((a -x)/(xa))/(x-a)

=-((x -a)/(xa))/(x-a)

=-(x -a)/((xa) (x-a))

=-(x -a)/((xa) (x²-a²))

=-(x -a)/((xa) (x -a)(x +a))

=-1/((xa) (x +a))

=-1/((xa) (a +x))