Question

Please sean f y g funciones de variable real, tales que f(x)=4(x-1) y g(X)= 6-x/2

Answer 1

The inverse function of the given functions are $f^{-1}(x)=\frac{x}{4}+1$ and $g^{-1}(x)$=-2x+6.

The given functions are f(x)=4(x-1) and g(x)=(6-x)/2.

We need to determine $f^{-1}$ and $g^{-1}$.

What is the inverse function?

In mathematics, an inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.x. A function f that has an inverse is called invertible and the inverse is denoted by $f^{-1}$.

Now, we can write f(x)=4(x-1) as y=4x-4

To find the inverse, interchange the variables and solve for y.

That is, x=4y-4

⇒x=4(y-1)

⇒(y-1)=x/4

⇒y=x/4 +1

⇒$f^{-1}(x)=\frac{x}{4}+1$

We can write g(x)=(6-x)/2 as y=(6-x)/2.

To find the inverse, interchange the variables and solve for y.

That is, x=(6-y)/2

⇒2x=6-y

⇒y=-2x+6

⇒$g^{-1}(x)$=-2x+6

Therefore, the inverse function of the given functions are $f^{-1}(x)=\frac{x}{4}+1$ and $g^{-1}(x)$=-2x+6.

To learn more about the inverse function visit:

brainly.com/question/5245372.

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