Question

if g(x )is a curve which is obtained by the reflection of f( x)=

Answer 1

d. .....................

Answer 2

Answer:

D. g(x) has no extremum

Step-by-step explanation:

We are given the function, $y=f(x)=\frac{e^x-e^{-x}}{2}$

Now, it is reflected across the line y=x i.e. we interchange y and x in the function and then find the value of y.

So, the new function is $x=\frac{e^y-e^{-y}}{2}$ i.e. $x=\sinh y$ i.e. $y=\sinh^{-1} x$

That is, $y=g(x)=\sinh^{-1} x$

After plotting the function g(x), we see that,

There is no tangent parallel to x-axis or y-axis. Moreover, the line y=-x is not tangent to the graph of g(x).

Hence, the function g(x) has no point of extrema.

So, option D is correct.