Functions Question 511
Which of the following functions is (are) injective maps?
Options:
A) $ f(x)=x^{2}+2,x\in (-\infty ,\infty ) $
B) $ f(x)=| x+2 |,x\in [-2,\infty ) $
C) $ f(x)=(x-4)(x-5),x\in (-\infty ,\infty ) $
D) $ f(x)=\frac{4x^{2}+3x-5}{4+3x-5x^{2}},x\in (-\infty ,\infty ) $
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Answer:
Correct Answer: B
Solution:
The function $ f(x)=x^{2}+2,x\in (-\infty ,\infty ) $ is not injective as $ f(1)=f(-1) $ but $ 1\ne -1. $ The function $ f(x)=(x-4)(x-5),x\in (-\infty ,\infty ) $ is not one-one as $ f(4)=f(5), $ but $ 4\ne 5. $ The function, $ f(x)=\frac{4x^{2}+3x-5}{4+3x-5x^{2}},x\in (-\infty ,\infty ) $ is also not injective as $ f(1)=f(-1),but1\ne -1. $ For the function, $ f(x)=| x+2 |,x\in [-2,\infty ). $ Let $ f(x)=f(y),x,y\in [-2,\infty )\Rightarrow | x+2 | =| y+2 | $ $ \Rightarrow x+2=y+2\Rightarrow x=y $ So, f is an injection.
BETA
