Question

If the function f(x) = -2/3 and g(x) = 3x + 1/2, then which of the following is a true statement?

1) f(g(0)) > 3
2) f(g(2)) = -1/2
3) f(g(8)) = 25/2
4) g(f(4)) < 14

Answer 1

If the function f(x) = -2/3 and g(x) = 3x + 1/2, the true statement is f(g(0)) = f(g(2)) = f(g(8)) = g(f(4)) = -2/3.

Step-by-step explanation:

The given functions are f(x) = -2/3 and g(x) = 3x + 1/2.

To find f(g(0)), substitute 0 into g(x):
f(g(0)) = f(3(0) + 1/2)
= f(1/2)
= -2/3

Similarly, to find f(g(2)), substitute 2 into g(x):
f(g(2)) = f(3(2) + 1/2)
= f(6 + 1/2)
= f(13/2)
= -2/3

For f(g(8)), substitute 8 into g(x):
f(g(8)) = f(3(8) + 1/2)
= f(25 + 1/2)
= f(51/2)
= -2/3

Finally, to find g(f(4)), substitute 4 into f(x):
g(f(4)) = g(-2/3)
= 3(-2/3) + 1/2
= -2 + 1/2
= -3/2

Therefore, the true statement is f(g(0)) = f(g(2)) = f(g(8)) = g(f(4)) = -2/3.