Find the range of the following functions.

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Find the range of the following functions. (1) f(x)=∣x+1∣+∣2x+1∣+∣2x−1∣+∣x−1∣f(x) = |x+1| + |2x+1| + |2x-1| + |x-1| . (2) f(x)=log⁡2(sin⁡x−cos⁡x+322)f(x) = \log_2 \left( \frac{\sin x - \cos x + 3\sqrt{2}}{\sqrt{2}} \right) . (3) f(x)=x2+3x+2f(x) = x^2 + 3x + 2 . (4) f(x)=ln⁡2x+3ln⁡x+5f(x) = \ln^2 x + 3 \ln x + 5 . (5) f(x)=3ln⁡x+2ex+3f(x) = 3 \ln x + 2e^x + 3 . (6) f(x)=3ln⁡2x+ln⁡2x+3f(x) = 3 \ln^2 x + \ln 2x + 3 .

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