Q67 / 160 · TS EAMCET 2024 (09 May Shift 2) · Mathematics

Match the functions givenin List-I with their relevant characteristics from List-II. Figure
The correct answer is

  • A
    A-II, B-III, C-IV, D-V
  • B
    A-V, B-I, C-II, D-III
  • C
    A-IV, B-II, C-I, D-V
  • Correct answer
    D
    A-IV, B-III, C-V, D-II

Solution

(A) $\sinh x=\frac{e^x-e^{-x}}{2}$ $\sinh (-x)=\frac{e^{-x}-e^x}{2}=-\sinh x$ $\therefore$ Odd function and range is $R$. (B) $\sec h(x)=\frac{2}{e^x+e^{-x}}$ $\operatorname{sech}(-x)=\frac{2}{e^{-x}+e^x}=\operatorname{sech}(x)$ $\therefore$ Even function. (C) $\tanh x=\frac{e^x-e^{-x}}{e^x+e^{-x}}$ $\therefore$ Odd function and range $(-1,1)$ (D) $\operatorname{cosech}^{-1} x=$ in $\left(\frac{1}{x}+\frac{\sqrt{1+x^2}}{|x|}\right)$ $\therefore$ Domain $x \neq 0$ and neither even nor odd function.

Hence, the correct answer is option: 'D'.

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