Answer: The correct conclusion is(B) The functions f(x) and g(x) are reflections over the y-axis.
Step-by-step explanation: Two functions f(x) and g(x) are given as follows:
We know that if f(-x) = g(x), then the functions are reflections over Y-axis and if - f(x) = g(x), then the functions are reflections over X-axis.
We have,
So, the function g(x) is a reflection of f(x) over Y-axis.
The graph of f(x) and g(x) are drawn in the attached file. From there, it is clear that the functions are reflections over Y-axis, not reflections over X-axis.
So, options (A) is incorrect and option (B) is correct.
From the table, we have
So, as the value of 'x' increases, the value of f(x) increases and value of y(x) decreases.
Therefore, f(x) is an increasing function and g(x) is a decreasing function. So, option (C) is incorrect.
Also, we have
So, both the functions have same initial value. So, option (D) is also incorrect.
Thus, the correct conclusion is (B) The functions f(x) and g(x) are reflections over the y-axis.
