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Liono4ka [1.6K]
3 years ago
5

Which of the following equations represents the inverse of y = e2x - 9?

Mathematics
2 answers:
finlep [7]3 years ago
8 0

Answer:

\frac{1}{2}ln(x+9) = y

Step-by-step explanation:

We have given an equation.

y = e^{2x} -9

We have to find the inverse of the equation.

Adding 9 to both sides of above equation, we have

y+9 = e^{2x} +9-9

y+9 = e^{2x}

Taking logarithms to both sides of above equation, we have

ln(y+9) = ln(e^{2x})

ln(y+9) = 2x

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

\frac{1}{2}ln(y+9) = x

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

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

Replacing y by x , we have

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

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

Keith_Richards [23]3 years ago
4 0

Answer:

y=\frac{1}{2} \ln(x+9)

Step-by-step explanation:

The given function is

y=e^{2x}-9

Interchange x and y.

x=e^{2y}-9

Solve for y.

x+9=e^{2y}

Take logarithm of both sides to base e.

\ln(x+9)=2y

Divide both sides by 2.

y=\frac{1}{2} \ln(x+9)

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