Question

f(x) =(e^6x)/8+(e^6x)

Find the inverse

Answer 1

f^(-1)(x) = (8 x)/(9 e^6)

Answer 2

@lawnphysics how did you get that answer?

Answer 3

y=e^(6x)(1+1/8)
ln(y)=6x+ln(9/8)
x=ln(y)/6-ln(9/8)/6

Answer 4

f(x)=(e^(6)x)/(8)+(e^(6)x)

To find the inverse of the function, interchange the variables and solve for f^(-1)(x).
x=(e^(6)f^(-1)(x))/(8)+(e^(6)f^(-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.
(e^(6)f^(-1)(x))/(8)+(e^(6)f^(-1)(x))=x

Reduce the expression (e^(6)f^(-1)(x))/(8) by removing a factor of
(f^(-1)(x)e^(6))/(8)+(e^(6)f^(-1)(x))=x

Remove the parentheses from the numerator.
(f^(-1)(x)e^(6))/(8)+e^(6)f^(-1)(x)=x

Arrange the variables alphabetically within the expression Z^(6)f^(-1)(x). This is the standard way of writing an expression.
(f^(-1)(x)e^(6))/(8)+f^(-1)(x)e^(6)=x

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 8. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
f^(-1)(x)e^(6)*(8)/(8)+(f^(-1)(x)e^(6))/(8)=x

Complete the multiplication to produce a denominator of 8 in each expression.
(8f^(-1)(x)e^(6))/(8)+(f^(-1)(x)e^(6))/(8)=x

Combine the numerators of all expressions that have common denominators.
(8f^(-1)(x)e^(6)+f^(-1)(x)e^(6))/(8)=x

Combine all like terms in the numerator.
(9f^(-1)(x)e^(6))/(8)=x

Multiply each term in the equation by 8.
(9f^(-1)(x)e^(6))/(8)*8=x*8

Simplify the left-hand side of the equation by canceling the common factors.
9f^(-1)(x)e^(6)=x*8

Multiply x by 8 to get 8x.
9f^(-1)(x)e^(6)=8x

Divide each term in the equation by 9e^(6).
(9f^(-1)(x)e^(6))/(9e^(6))=(8x)/(9e^(6))

Simplify the left-hand side of the equation by canceling the common factors.
f^(-1)(x)=(8x)/(9e^(6))

Answer 5

by inverse you mean that f(inverse)=1 or f*inverse=1?

Answer 6

is f^-1 the same as y in this case?

Answer 7

this is it, your good to go

Answer 8

Thanks. I am trying to put this into maple ta, but it is giving me a wrong answer :(