Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
junior college 1 | H2 Maths
3 Answers Below
Anyone can contribute an answer, even non-tutors.
hello can anyone help me with this question?
Date Posted: 4 years ago
Views: 644
f(x) = (px+q)/(x + r)
If f(x) is even, f(-x) = f(x)
(p(-x) + q)/((-x) + r) = (px + q)/(x + r)
(q - px)(x + r) = (px + q)(r - x)
qx + qr - px² - pxr = pxr - px² + qr - qx
2qx - 2pxr = 0
qx - prx = 0
x(q - pr) = 0
x = 0 or q - pr = 0 → q = pr
So when x = 0, f(x) = f(0)
= (p(0) + q)/(0 + r)
= q/r
When q = pr
f(x) = (px + pr)/(x + r)
= p(x + r)/(x + r)
= p
(Proved)
If f(x) is even, f(-x) = f(x)
(p(-x) + q)/((-x) + r) = (px + q)/(x + r)
(q - px)(x + r) = (px + q)(r - x)
qx + qr - px² - pxr = pxr - px² + qr - qx
2qx - 2pxr = 0
qx - prx = 0
x(q - pr) = 0
x = 0 or q - pr = 0 → q = pr
So when x = 0, f(x) = f(0)
= (p(0) + q)/(0 + r)
= q/r
When q = pr
f(x) = (px + pr)/(x + r)
= p(x + r)/(x + r)
= p
(Proved)
a < b ⇔f(a) < f(b)
when x = a, f(x) = f(a)
When x = b, f(x) = f(b)
When x = f(a), f-¹(x)
= f-¹(f(a))
= a
When x = f(b), f-¹(x)
= f-¹(f(b))
= b
Since a < b,
f-¹(f(a)) < f-¹(f(b))
Since f(a) < f(b),
This means f(a) < f(b) ⇔f-¹(f(a)) < f-¹(f(b))
when x = a, f(x) = f(a)
When x = b, f(x) = f(b)
When x = f(a), f-¹(x)
= f-¹(f(a))
= a
When x = f(b), f-¹(x)
= f-¹(f(b))
= b
Since a < b,
f-¹(f(a)) < f-¹(f(b))
Since f(a) < f(b),
This means f(a) < f(b) ⇔f-¹(f(a)) < f-¹(f(b))
See 3 Answers
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
for part (a) i think it is like that? since f(x) = f(-x) then just subst x with -x then equate and simplify
Date Posted:
4 years ago
x should not be crossed out on both sides.
That eliminates a possible solution, whereby x = 0
That eliminates a possible solution, whereby x = 0
thank you !!
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
ok idk how to use all the math terms and all but the geist it this. since f(x) is strictly increasing, for a
Date Posted:
4 years ago
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
oh yaaa !! there is another answer maybe?? since the qn say for some values of k so k is either q or q/r
Date Posted:
4 years ago
360 Tutoring Program