Question

The table below shows the values for the function y = f(x).

x,-3-1,0,5,6

y,5,-4,2,-8,3

if.g(x)=1/2f(x), which of the following are solutions to g(x)? Select all that apply.

(-3,5.5)

(-1,-2)

(0,4)

(5,-8)

(6,3/2)

Answer 1

To find the solutions to g(x), we need to substitute each x-value into the equation g(x) = 1/2f(x) and check if it matches the corresponding y-value.

For (-3, 5.5):
g(-3) = 1/2f(-3) = 1/2(5) = 2.5, which does not match the y-value of 5. Therefore, (-3, 5.5) is not a solution to g(x).

For (-1, -2):
g(-1) = 1/2f(-1) = 1/2(-4) = -2, which matches the y-value of -4. Therefore, (-1, -2) is a solution to g(x).

For (0, 4):
g(0) = 1/2f(0) = 1/2(2) = 1, which does not match the y-value of 2. Therefore, (0, 4) is not a solution to g(x).

For (5, -8):
g(5) = 1/2f(5) = 1/2(-8) = -4, which does not match the y-value of -8. Therefore, (5, -8) is not a solution to g(x).

For (6, 3/2):
g(6) = 1/2f(6) = 1/2(3) = 1.5, which matches the y-value of 3. Therefore, (6, 3/2) is a solution to g(x).

Therefore, the solutions to g(x) are (-1, -2) and (6, 3/2).