The inverse of the function $f(x) = \frac{{{e^x} - {e^{ - x}}}}{{{e^x} + {e^{ - x}}}} + 2$ is given by
The inverse of the function $f(x) = \frac{{{e^x} - {e^{ - x}}}}{{{e^x} + {e^{ - x}}}} + 2$ is given by
- A
${\log _e}{\left( {\frac{{x - 2}}{{x - 1}}} \right)^{1/2}}$
- B
${\log _e}{\left( {\frac{{x - 1}}{{3 - x}}} \right)^{1/2}}$
- C
${\log _e}{\left( {\frac{x}{{2 - x}}} \right)^{1/2}}$
- D
${\log _e}{\left( {\frac{{x - 1}}{{x + 1}}} \right)^{ - 2}}$
Similar Questions
If $f$ be the greatest integer function and $g$ be the modulus function, then $(gof)\left( { - \frac{5}{3}} \right) - (fog)\left( { - \frac{5}{3}} \right) = $
If $f$ be the greatest integer function and $g$ be the modulus function, then $(gof)\left( { - \frac{5}{3}} \right) - (fog)\left( { - \frac{5}{3}} \right) = $
Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ given by $f(1)=a, \,f(2)=b$ and $f(3)=c .$ Find $f^{-1}$ and show that $\left(f^{-1}\right)^{-1}=f$.
Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ given by $f(1)=a, \,f(2)=b$ and $f(3)=c .$ Find $f^{-1}$ and show that $\left(f^{-1}\right)^{-1}=f$.
Which of the following functions is inverse of itself
Which of the following functions is inverse of itself
Show that $f:[-1,1] \rightarrow R ,$ given by $f(x)=\frac{x}{(x+2)}$ is one-one. Find the inverse of the function $f:[-1,1] \rightarrow$ Range $f$
$($ Hint: For $y \in $ Range $f$, $y=f(x)=\frac{x}{x+2}$, for some $x$ in $[-1,1]$, i.e., $x=\frac{2 y}{(1-y)})$
Show that $f:[-1,1] \rightarrow R ,$ given by $f(x)=\frac{x}{(x+2)}$ is one-one. Find the inverse of the function $f:[-1,1] \rightarrow$ Range $f$
$($ Hint: For $y \in $ Range $f$, $y=f(x)=\frac{x}{x+2}$, for some $x$ in $[-1,1]$, i.e., $x=\frac{2 y}{(1-y)})$
If $a * b=10$ ab on $Q^{+}$ then find the inverse of 0.01
If $a * b=10$ ab on $Q^{+}$ then find the inverse of 0.01