Question

The function g(x) =8(4x) is reflected across the x-axis to create f(x) what is the equation for f(x)

Answer 1

Answer:f(x)= -8 (4x) will be the reflected function across x-axis for the function g(x).

Explanation:  since we know that the image or reflection of x along x-axis = -x

That is, when we talk about a function's reflection across any axis then we have to replace variable according to that axis. For example if you have a line x=3 in positive x-axis  then you can also draw a similar line x=-3 in negative x-axis. so, you can say, x=-3 is the reflection of x=3 along x axis.

Similarly, for an another line y=3, y=-3 is a reflection.

thus in the case of g(x) we can find the reflection across x-axis after replacing x by -x.  

we have g(x) =8(4x)  

replace x by -x we get g(-x)= 8(4×-x)= 8(-4x)=-8(4x)

so -8(4x) is the reflection of g(x)

but according to the question f(x) is the reflection of g(x) across x-axis.

Thus, f(x)=-8(4x)

Answer 2

-8 is the answer
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