Question

f(x)=sqrt(5-e^(2x))

Answer 1

I need the domain

Answer 2

make sure
\[5-e^{2x}\geq 0\]

Answer 3

ok but im stuck there

Answer 4

\[5\geq e^{2x}\]
\[\ln(5)\geq 2x\]
\[\frac{\ln(5)}{2}\geq x\]

Answer 5

so the domain would be

Answer 6

I don't know how to write the domain for it because I keep getting it wrong

Answer 7

maybe they want a decimal?

Answer 8

How can I write it they give me this format ([ ]) U ([ ])

Answer 9

f(x)=~(5-e^(2x))

The domain of an expression is all real numbers except for the regions where the expression is undefined. This can occur where the denominator equals 0, a square root is less than 0, or a logarithm is less than or equal to 0. All of these are undefined and therefore are not part of the domain.
(5-e^(2x))<0

Solve the equation to find where the original expression is undefined.
x>(ln(5))/(2)_x<Z>APPR<z>0.8047

The domain of the rational expression is all real numbers except where the expression is undefined.
x<=(ln(5))/(2)_(-<Z>I<z>,(ln(5))/(2)]

Answer 10

\[x<=(\ln(5))/(2)_(-<Z>I<z>,(\ln(5))/(2)]\]

Answer 11

ok thanks

Answer 12

how can i find the inverse of that same question?

Answer 13

i get a big equation that doesnt make any sense

Answer 14

Inverse:
f(x)=~(5-e^(2x))

To find the inverse of the function, interchange the variables and solve for f^(-1)(x).
x=~(5-e^(2f)-1^(x))

Since f^(-1)(x) is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
~(5-e^(2f)-1^(x))=x

To remove the radical on the left-hand side of the equation, square both sides of the equation.
(~(5-e^(2f)-1^(x)))^(2)=(x)^(2)

Simplify the left-hand side of the equation.
5-e^(2f)-1^(x)=(x)^(2)

Expand the exponent (2) to the expression.
5-e^(2f)-1^(x)=(x^(2))

Remove the parentheses around the expression x^(2).
5-e^(2f)-1^(x)=x^(2)

Since 5 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 5 from both sides.
-e^(2f)-1^(x)=-5+x^(2)

Reorder the polynomial -5+x^(2) alphabetically from left to right, starting with the highest order term.
-e^(2f)-1^(x)=x^(2)-5

Multiply each term in the equation by -1.
-e^(2f)-1^(x)*-1=x^(2)*-1-5*-1

Multiply -e^(2f^(-1)(x)) by -1 to get e^(2f^(-1)(x)).
e^(2f)-1^(x)=x^(2)*-1-5*-1

Multiply x^(2) by -1 to get -x^(2).
e^(2f)-1^(x)=-x^(2)-5*-1

Multiply -5 by -1 to get 5.
e^(2f)-1^(x)=-x^(2)+5

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(e^(2f)-1^(x))=ln(-x^(2)+5)

The natural logarithm of e^(2f^(-1)(x)) is 2f^(-1)(x).
(2f^(-1)(x))=ln(-x^(2)+5)

Remove the parentheses around the expression 2f^(-1)(x).
2f^(-1)(x)=ln(-x^(2)+5)

Divide each term in the equation by 2.
(2f^(-1)(x))/(2)=(ln(-x^(2)+5))/(2)

Cancel the common factor of 2 in (2f^(-1)(x))/(2).
(<X>2<x>f^(-1)(x))/(<X>2<x>)=(ln(-x^(2)+5))/(2)

Remove the common factors that were cancelled out.
f^(-1)(x)=(ln(-x^(2)+5))/(2)

Answer 15

ok thanks