## dainel40 2 years ago f(x)=sqrt(5-e^(2x))

1. dainel40

I need the domain

2. satellite73

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

3. dainel40

ok but im stuck there

4. satellite73

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

5. dainel40

so the domain would be

6. dainel40

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

7. satellite73

maybe they want a decimal?

8. dainel40

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

9. some_someone

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)]

10. some_someone

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

11. dainel40

ok thanks

12. dainel40

how can i find the inverse of that same question?

13. dainel40

i get a big equation that doesnt make any sense

14. some_someone

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)

15. dainel40

ok thanks