Maths · One-one, into and onto functions
If a function \rightarrow \boldsymbol{B} \) defined by =x^{2}-4 x+5 \) is a bije
If a function \( \boldsymbol{f}:(2, \infty) \rightarrow \boldsymbol{B} \) defined by \( f(x)=x^{2}-4 x+5 \) is a bijection, then \( \boldsymbol{B}= \)
- A. \( R \)
- B. \( [1, \infty) \)
- C. (0,1]
- D. [0,1]
Step-by-step solution
The function f(x) = x^2 - 4x + 5 = (x-2)^2 + 1 on domain (2, ∞) is strictly increasing and has range (1, ∞). For f to be bijective (one-one and onto), the codomain B must equal the range. Among the options, only [1, ∞) contains the actual range (1, ∞) and is the only plausible choice, though it includes 1 which is not attained. Options A, C, D do not match the range.
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