Question

Show that (f o g)(x) = (g o f)(x) = x

Answer 1

Answer:

$- \frac{2[1 - x]}{3} = g[f(x)] \\ \\ \frac{3x}{2 - x} = f[g(x)]$

Step-by-step explanation:

They are not.

For the g[f(x)] function, you substitute ³/ₓ ₋ ₁ from the f(x) function in for x in the g(x) function to get this:

$\frac{2}{ \frac{3}{x - 1}}$

Then, you bring x - 1 to the top while changing the expression to its conjugate [same expressions with opposite symbols]:

$- \frac{2[1 - x]}{3}$

You could also do this [attaching another negative would make that positive].

For the f[g(x)] function, ²/ₓ from the g(x) function for x in the f(x) function to get this:

$\frac{3}{ \frac{2}{x} - 1}$

Now, if you look closely, ²/ₓ is written as 2x⁻¹, and according to the Negative Exponential Rule, you bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM NEGATIVE TO POSITIVE:

$\frac{3x}{2 - x}$

When this happens, x leaves the two and gets attached to the three, and 1 gets an x attached to it.

I am joyous to assist you anytime.