Asked by Raj
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.
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.
Answers
Answered by
Reiny
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
= 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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.