If \(f(x)=\dfrac{a}{x+2}\) , solve for the value of \(a\) so that \(f(0)=f^{-1}(3a).\)
please help anyone???
Hey there guest.
f(0)=a/2
note that f^-1 is the recipricol of f
knowing that, f(3a)=a/3a+2. f^-1(3a)= 3a+2/a
f(0)=f^-1, so a/2=3a+2/a. Cross multiplying gives a^2=6a+4
a^2-6a-4=0
Completing the square time:
a^2-6a+9=13
(a-3)^2=13
a-3=+/-sqrt13
a=+/-sqrt3 + 3
Hope this helps
f-1 means inverse rather than reciprocal, so if f(x) = a/(x+2) then f-1(x) = a/x - 2
f(0) = a/2
f-1(3a) = 1/3 - 2 = -5/3
So a/2 = -5/3 or a = -10/3