FINDING INVERSE OF EXPONENTIAL FUCNTIONS

To find inverse of a linear function, we follow the steps given below.

Step 1 :

The given equation will be in the form y =, Derive the equation for x = .

Step 2 :

After solving for x, change x as f^-1(x) and y as x.

Relationship between f(x) and and f^-1(x) :

Domain of the function f(x) = Range of f^-1(x)

Range of the function f(x) = Domain of f^-1(x)

Find the inverse of exponential function :

Problem 1 :

y = 10^x/2

Solution :

y = 10^x/2

log₁₀y = x/2

2log₁₀y = x

Using the rule log mⁿ = n logm

log₁₀y² = x

Replace x = f^-1(x) and y = x

f^-1(x) = log₁₀x²

f^-1(x) = log x²

Problem 2 :

y = 4^x/3

Solution :

y = 4^x/3

log₄y = x/3

3 log₄y = x

Using the rule log mⁿ = n logm

log₄y³ = x

Replace x = f^-1(x) and y = x

f^-1(x) = log₄x³

Problem 3 :

y = 3^x + 4

Solution :

y = 3^x + 4

y - 4 = 3^x

log₃ (y - 4) = x

x = log₃ (y - 4)

Replace x = f^-1(x) and y = x

f^-1(x) = log₃ (x - 4)

Problem 4 :

y = 6^x + 2

Solution :

y = 6^x + 2

y - 2 = 6^x

log₆ (y - 2) = x

x = log₆ (y - 2)

Replace x = f^-1(x) and y = x

f^-1(x) = log₆ (x - 2)

Problem 5 :

Solution :

Problem 6 :

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Problem 7 :

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Problem 8 :

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Problem 9 :

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Problem 10 :

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