Respuesta :

kudzordzifrancis

ANSWER

B. The functions f(x) and g(x) because f(g(x))=g(f(x))=x

EXPLANATION

The given functions are:

[tex]f(x) = 2x - 2[/tex]

and

[tex]g(x) = \frac{1}{2}x + 1[/tex]

If f(x) and g(x) are inverses, then

f(g(x))=x

[tex]f(g(x))=f( \frac{1}{2} x + 1)[/tex]

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

Expand the parenthesis to obtain,

[tex]f(g(x))=x + 2- 2[/tex]

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

Also,

[tex]g(f(x)) = g(2x - 2)[/tex]

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

[tex]g(f(x)) = x - 1+ 1[/tex]

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

Hence f(x) and g(x) are inverses

luisejr77

Answer: Option B

Then The functions f(x) and g(x) are inverses because [tex]f(g(x))=g(f(x))=x[/tex]

Step-by-step explanation:

To answer this question we must make the composition of f (x) and g (x)

We found

[tex]f (g(x))[/tex]

We know that

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

By definition if two functions f and g are inverses then it follows that:

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

So if [tex]f(g(x)) = x[/tex] f and g are inverse

To find  [tex]f(g(x))[/tex] enter the function g(x) within  the function f(x) as shown below

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

Now

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

Observe that

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

Then The functions f(x) and g(x) are inverses because [tex]f(g(x))=g(f(x))=x[/tex]