Functions Flashcards
1
Q
Where does the hyperbola xy=c^2 intersect the line y=x?
A
(c,c) and (-c,-c)
2
Q
The circle x^2 +y^2 = r^2 has centre the origin and radius r. The circle is shifted so that its centre is at C(h,k). The point P(x,y) lies on the circle with centre C(h,k) and radius r. That is, P lies on the shifted circle in part a. This time, use the distance formula to find the radius PC to obtain the equation of the circle.
A
(x-h)^2 + (y-k)^2 = r^2
3
Q
Let f(x) = 2x+3 and g(x) = ax+b, where b is a constant.
Find the values of a and b so that g(f(x)) = x, for all x.
A
a = 1/2
b = -3/2
