Answer:
A, C, E & F are true
Step-by-step explanation:
We are given the functions;
g(x) = x² and h(x)= -x²
Let's analyze the options;
A) For any value of x,g(x) will always be greater than h(x);
Let's put x = 1 in both functions;
g(x) = 1² = 1
h(x) = - (1)² = - 1
Let's try a negative number say -1:
g(x) = (-1)² = 1
h(x) = -(-1)² = -1
In both cases, we see that g(x) > h(x) and so the statement is true.
B) For any value of x,h(x) will always be greater than g(x); As seen in A above, for any value of x, h(x) will always be greater than g(x). And so this statement here is wrong.
C) g(x) > h(x) for x = -1;
As seen in A above, at x = -1, g(x) > h(x).
Thus, this statement is true
D) g(x) < h(x) for x = 3;
g(x) = (3)² = 9
h(x) = -(3)² = -9
g(x) is not less than h(x) and so the statement is not correct.
E) For positive values of x, g(x) > h(x).
We have tried positive numbers at x = 1 and x = 3 in previous answers above and in both cases, g(x) > h(x).
Thus, statement is true.
F) For negative values of x, g(x) > h(x).
We have seen earlier that at a negative value of x = -1, g(x) > h(x)
Let's try x = -2
g(x) = (-2)² = 4
h(x) = -(-2)² = -4
Still seeing that g(x) > h(x).
Thus the statement is true.
