Consider the function f :[1, ∞) arrow(0,1], f ( t )=(1/1+ t 2). Which one of the following is TRUE?

Question

Consider the function f :[1, ∞) arrow(0,1], f ( t )=(1/1+ t 2). Which one of the following is TRUE? (A) f is bijective (B) f is one-to-one but not onto (C) fis onto but not one-to-one (D) fis neither one-to-one nor onto

Tardigrade Admin · Accepted Answer

Correct answer is (b) f is one-to-one but not onto

Q. Consider the function $f : [1, \infty) \to (0, 1], f (t) = \frac{1}{1 + t ^{2}}$ . Which one of the following is TRUE?

$f$ is bijective

f is one-to-one but not onto

fis onto but not one-to-one

fis neither one-to-one nor onto

Correct answer is (b) f is one-to-one but not onto

Q. Consider the function f:[1,∞)→(0,1],f(t)=1+t21​. Which one of the following is TRUE?

f is bijective

f is one-to-one but not onto

fis onto but not one-to-one

fis neither one-to-one nor onto

Correct answer is (b) f is one-to-one but not onto

Q. Consider the function $f : [1, \infty) \to (0, 1], f (t) = \frac{1}{1 + t ^{2}}$ . Which one of the following is TRUE?

$f$ is bijective