If $f(x)=\frac{x-3}{x+1}$, then $f(f(x))

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $f(x)=\frac{x-3}{x+1}$, then $f(f(x))$ equals:

Options:

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

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

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

$\frac{4+x}{1-x}$

Correct Answer:

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

Explanation:

$f[f(x)]=f(x)-3f(x)+1$

$=\frac{\frac{x-3}{x+1}-3}{\frac{x-3}{x+1}+1}$

$=\frac{x-3-3x-3}{x-3+x+1}$

$=\frac{3+x}{1-x}$