The domain and range for the function f(x)=e^ |x| x are domain = IR

MHT CET 2022 Mathematics question

The domain and range for the function are domain = IR

(A)range = , domain = IR
(B)range = , domain = IR
(C)range = IR, domain = IR
(D)range = , domain = IRCorrect

Answer: (D)

Solution

is defined for every real , so the domain is IR. Let . It is continuous, , and as at the points we get while at we get . By continuity takes every real value, so

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Question ID VK-093748