Express f(f(x)) as a single simplified fraction.f(x) = x/x+1

Question

Clarence Mills · Accepted Answer

All you have to do to solve this problem is plug in f(x) into itself.
if f(x)= x/x+1, then

f (f (x)) = \frac{(x / x + 1)}{(x / x + 1) + 1}

In order to add the whole denominator, 1 can be substituted for

\frac{x + 1}{x + 1}

which would result in the new whole equation being

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

Then, in order to make one nice fraction, you take the top equation and leave it as it is. You then multiply that by bottom fraction flipped. If this is done, the equation will look like

\frac{x}{x + 1} \times \frac{x + 1}{2 x + 1}

When you have this, the x+1 in the denominator of the first fraction and the numerator of the second fraction cancel out leaving

\frac{x}{1} \times \frac{1}{2 x + 1}

which is turn simplifies to the answer of

\frac{x}{2 x + 1}

.
That is the simplied fraction of the original equation.

Natalya Mayer · Accepted Answer

f  (  x  )  =  frrac      x        x    +    1    f  (  f  (  x  )  )  =  f  (      x          x      +      1        )  =            x              x        +        1                            x                  x          +          1                    +      1        =            x              x        +        1                            x        +        x        +        1                    x        +        1              =      x          x      +      1        ∗            x      +      1              2      x      +      1        =      x          2      x      +      1        f  (  f  (  x  )  )  =      x          2      x      +      1

Express f(f(x)) as a single simplified fraction. f(x) = x/x+1

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