Question

This function f(x) has a domain of x = {-a, -b, a, b}.

In order, the x values are -a, -b, b, a.

In order, the f(x) values are 3c + 1, 2d - 5, 4d + 3, 6 - 2c.

Which values of c and d make this an even function?

a. c = -7 and d = 1/3
b. c = 5 and d = 1/3
c. c = -5 and d = -4
d. c = 1 and d = -4
e. c = -7 and d = -4​

Answer 1

d. c = 1 and d = -4

Explanation:

If a function is even, then f(-x) = f(x). Graphically, this means it's symmetrical about the y-axis.

f(-a) = f(a)

3c + 1 = 6 − 2c

5c = 5

c = 1

f(-b) = f(b)

2d − 5 = 4d + 3

-2d = 8

d = -4

Therefore, c = 1 and d = -4.