Respuesta :

We are given

[tex]f(x)=cos(\frac{x}{2} )[/tex]

[tex]g(x)=cos(x )[/tex]

now, we can find relation between f(x) and g(x)

Since, g(x) is parent function

so, we get

[tex]f(x)=g(\frac{x}{2})[/tex]

Since, there is change in x as x/2

so, x is divide by 2

So, it is horizontal stretch by 2 units..........Answer

The transformations required to obtain the graph of the function f(x) from the graph of the function g(x) are by stretching the function g(x) horizontally by 2.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given to us

[tex]g(x) = cos(x)[/tex]

[tex]f(x) = cos(\dfrac{x}{2})[/tex]

We know that g(x) is the parent function of f(x), therefore, we can write

[tex]f(x) = g(\dfrac{x}{2})[/tex]

Checking the function,

g(x) = cos x

substituting the value of x as

[tex]\dfrac{x}{2}[/tex]

we get,

[tex]g(\dfrac{x}{2}) = cos(\dfrac{x}{2})[/tex]

Hence, the transformations required to obtain the graph of the function f(x) from the graph of the function g(x) are by stretching the function g(x) horizontally by 2.

Learn more about Transformation:

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