Chapter 5: Q 60. (page 257)

If $f (x) = \frac{x + 1}{x - 1}$ find $(f o f) (x)$ .

Short Answer

Expert verified

The value of $(f o f) (x) = x$ .

Step by step solution

Step 1. Given information

$f (x) = \frac{x + 1}{x - 1}$ and the function $(f o f) (x) = f (f (x))$

Step 2. The given function written as.

$f (f (x)) = \frac{\frac{x + 1}{x - 1} + 1}{\frac{x + 1}{x - 1} - 1}$

Step 3. Simplify the given function.

$f (f (x)) = \frac{\frac{x + 1}{x - 1} + 1}{\frac{x + 1}{x - 1} - 1} f (f (x)) = \frac{\frac{x + 1 + x - 1}{x - 1}}{\frac{x + 1 - x + 1}{x - 1}} f (f (x)) = \frac{\frac{2 x}{x - 1}}{\frac{2}{x - 1}} f (f (x)) = x$

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If $f (x) = \frac{x + 1}{x - 1}$ find $(f o f) (x)$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The given function written as.

Step 3. Simplify the given function.

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If f(x)=x+1x-1find (fof)(x).

Short Answer

Step by step solution

Step 1. Given information

Step 2. The given function written as.

Step 3. Simplify the given function.

One App. One Place for Learning.

Most popular questions from this chapter

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If $f (x) = \frac{x + 1}{x - 1}$ find $(f o f) (x)$ .