Respuesta :

kudzordzifrancis

Answer:

[tex]y=\frac{1}{2} \ln(x+9)[/tex]

Step-by-step explanation:

The given function is

[tex]y=e^{2x}-9[/tex]

Interchange x and y.

[tex]x=e^{2y}-9[/tex]

Solve for y.

[tex]x+9=e^{2y}[/tex]

Take logarithm of both sides to base e.

[tex]\ln(x+9)=2y[/tex]

Divide both sides by 2.

[tex]y=\frac{1}{2} \ln(x+9)[/tex]

zainebamir540

Answer:

[tex]\frac{1}{2}ln(x+9) = y[/tex]

Step-by-step explanation:

We have given an equation.

[tex]y = e^{2x} -9[/tex]

We have to find the inverse of the equation.

Adding 9 to both sides of above equation, we have

[tex]y+9 = e^{2x} +9-9[/tex]

[tex]y+9 = e^{2x}[/tex]

Taking logarithms to both sides of above equation, we have

[tex]ln(y+9) = ln(e^{2x})[/tex]

[tex]ln(y+9) = 2x[/tex]

Dividing by 2 to both sides of above equation, we have

[tex]\frac{1}{2}ln(y+9) = x[/tex]

Putting x  = f⁻¹(y) in above equation ,we have

[tex]\frac{1}{2} ln(y+9) = f^{-1}(y)[/tex]

Replacing y by x , we have

[tex]\frac{1}{2}ln(x+9) = f^{-1}(x)[/tex]

[tex]\frac{1}{2}ln(x+9) = y[/tex] which is the answer.

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