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topjm [15]
2 years ago
15

HELP{

Mathematics
2 answers:
sertanlavr [38]2 years ago
4 0

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:

f(x)=2^x,~~~~~~~g(x)=\left(\dfrac{1}{2}\right)^x.

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,

f(-x)=2^{-x}=\left(\dfrac{1}{2}\right)^x=g(x),\\\\-f(x)=-2^x\neq g(x).

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

f(-2)=\dfrac{1}{4},~~f(-1)=\dfrac{1}{2},~~f(0)=1,~~f(1)=2,~~f(2)=4,\\\\g(-2)=4,~~g(-1)=2,~~g(0)=1,~~g(1)=\dfrac{1}{2},~~g(2)=\dfrac{1}{4}.

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

f(0)=g(0)=1.

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.

TiliK225 [7]2 years ago
4 0

Answer:

The correct answer is B) The functions f(x) and g(x) are reflections over the y-axis.

Step-by-step explanation:

Hope this helps! :)

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