Respuesta :

W0lf93
From the question we have that f(x) = -1/2 sin 5x and g(x) = 4 sin5x
Let's try to calculate -8f(x)
- 8f(x) = -8 (-1/2 sin 5x)
This becomes 4sin 5x
Since the function g(x) is -8 times f(x)
Hence g(x) = -8f(x)

Answer:

Hence, the required relationship is: [tex]-8(f(x))=g(x)[/tex]

Step-by-step explanation:

We have been given two functions:

[tex]f(x)=-\frac{1}{2}sin 5x[/tex]

And [tex]g(x)=4sin 5x[/tex]

We can see that angle is same that is sin 5x

So, for a relationship between both the functions we need to relate the amplitude that is [tex]y=a sinbt[/tex]  (1)

Where, a is amplitude.

If we compare two functions with (1) amplitude of f(x) is -1/2 and g(x) is 4

So, if we multiply -8 with f(x) that is:

[tex]-8(f(x))=-8(-\frac{1}{2}sin 5x)[/tex]

[tex]\Rightarrow -8(f(x))=4sin 5x[/tex]

[tex]\Rightarrow -8(f(x))=g(x)[/tex]

Hence, the required relationship is: [tex]-8(f(x))=g(x)[/tex]

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