Question

type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.

pic below

Answer 1

Answer:

• To determine the inverse of the given function,

Change f(x) to y , switch x and y , and solve for y.

• The resulting function may be written as:

                   $f^{-1}x=\dfrac{\ln (x+4)}{2}$

Step-by-step explanation:

We know that while finding the inverse of a function the following steps are to be followed:

• We first put f(x)=y

• Then we interchange x and y in the expression.

• and then we finally solve for y.

We are given a function f(x) by:

$f(x)=e^{2x}-4$

Now, we put

$f(x)=y$

i.e.

$e^{2x}-4=y$

Now, we interchange x and y as follows:

$e^{2y}-4=x$

and finally we solve for y

i.e.

$e^{2y}=x+4$

Taking logarithmic function both the side of the equation we get:

$2y=\ln (x+4)\\\\i.e.\\\\y=\dfrac{\ln (x+4)}{2}$

i.e.

$f^{-1}x=\dfrac{\ln (x+4)}{2}$