The function Q(x) has been transformed from the function f(x) = x^4. The mapping rule for the
function can be written as (2x + c, 4y + d). If the coordinate(1/2 ,1/16) on the function f(x) is
transformed to (3,5) on Q(x), determine the value of c and d.
To determine the values of c and d, we need to find the mapping rule that transforms the point (1/2 ,1/16) on the function f(x) to the point (3,5) on Q(x).
Let's start by substituting the coordinates of the point (1/2, 1/16) into the mapping rule (2x + c, 4y + d):
2 * (1/2) + c = 3 (equation 1)
4 * (1/16) + d = 5 (equation 2)
Simplifying equation 1:
1 + c = 3
c = 3 - 1
c = 2
Now, let's simplify equation 2:
1/4 + d = 5
d = 5 - 1/4
d = 5 - 0.25
d = 4.75
Therefore, the value of c is 2 and the value of d is 4.75.