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finlep [7]
3 years ago
5

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

Mathematics
2 answers:
schepotkina [342]3 years ago
8 0
I need you to be more specific
valentinak56 [21]3 years ago
4 0
<h2>Answer:</h2>
  • 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}

<h2>Step-by-step explanation:</h2>

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}

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