Question

Demuestre que ( f ᵒ g )(x) = ( g ᵒ f )(x) = x a) sabiendo que f(x) = 2x y g(x) = x/2 b) sabiendo que f(x) = 2x – 6 y g(x) = (x + 6)/2

Answer 1

Answer:

The answer is the demonstration, which is in the step-by-step explanation.

Step-by-step explanation:

Composite functions:

( f ᵒ g )(x) = f(g(x))

( g ᵒ f )(x) = g(f(x))

a)

f(x) = 2x

g(x) = x/2

$f(g(x)) = f(\frac{x}{2}) = 2\frac{x}{2} = x$

$g(f(x)) = g(2x) = \frac{2x}{2} = x$

Then

$f(g(x)) = g(f(x)) = x$

b)

f(x) = 2x - 6

g(x) = (x + 6)/2

$f(g(x)) = f(\frac{x+6}{2}) = 2\frac{x+6}{2} - 6 = x + 6 - 6 = x$

$g(f(x)) = g(2x - 6) = \frac{2x - 6 + 6}{2} = \frac{2x}{2} = x$

Then

$f(g(x)) = g(f(x)) = x$