f(g(x))
= f(9/(2-x))
= 4(9/(2-x)) - 2k
so 4(9/(2-x)) - 2k = x
multiply by 2-x
36 - 2k(2-x) = x(2-x)
36 - 4k + 2kx = 2x - x^2
x^2 + x(2k - 2) + 36 - 4k = 0
to have 2 equal roots, the discriminant has to be zero
(2k-2)^2 - 4(1)(36-4k) = 0
4k^2 - 8k + 4 - 144 + 16k = 0
4k^2 + 8k - 140 = 0
k^2 + 2k - 35 = 0
(k+7)(k-5) = 0
k = -7 or k = 5
Functions f and g are defined by
f(x)=4x-2k
g(x)=9/(2-x)
i.Find the values of k for which the equation fg(x)=x has two equal roots.
1 answer
1 answer