If f(x) = (x-1)/(x+1), find f(f(x)) — JEE Mathematics
If $f(x) = \frac{x-1}{x+1}$, find $f(f(x))$.
1 Answer
SSophiaMiller84
✓ Accepted
· 2mo ago
▲ 4
Substitute $f(x)$ into itself:
$$f(f(x)) = \frac{f(x) - 1}{f(x) + 1} = \frac{\frac{x-1}{x+1} - 1}{\frac{x-1}{x+1} + 1}$$
Simplify the numerator and denominator by multiplying by $(x+1)$:
$$Numerator = (x - 1) - (x + 1) = -2$$
$$Denominator = (x - 1) + (x + 1) = 2x$$
$$f(f(x)) = \frac{-2}{2x} = -\frac{1}{x}$$
Answer: $-\frac{1}{x}$
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Discussion (4)
KS
This finally made it click for me — thank you!
PI
Clean and to the point. Bookmarking this for revision.
RV
This is exactly the kind of step-by-step I needed. Respect.
S
For revision — the key formula used here comes up almost every year.