Question

How is the function f(x)=-1/2sin5x related to the function g(x)=4sin5x?

Answer 1

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 2

Answer:

Hence, the required relationship is: $-8(f(x))=g(x)$

Step-by-step explanation:

We have been given two functions:

$f(x)=-\frac{1}{2}sin 5x$

And $g(x)=4sin 5x$

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 $y=a sinbt$  (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:

$-8(f(x))=-8(-\frac{1}{2}sin 5x)$

$\Rightarrow -8(f(x))=4sin 5x$

$\Rightarrow -8(f(x))=g(x)$

Hence, the required relationship is: $-8(f(x))=g(x)$