Finding Inverse Functions

Linear Functions

100

Find the inverse. 

f(x) = 5x - 5

f^-1(x) = 1/5x + 1

200

Find the inverse.

f(x) = 0.5x + 10

f^-1(x) = 2x - 20

300

Find the inverse.

f(x) = (x-2) / 3

f^-1(x) = 3x + 2

400

Find f^-1(6) if f(x) = 3x + 6

0

Radical Functions

100

Find the inverse.

f(x) = x^1/2 

f^-1(x) = x²

200

Find the inverse.

f(x) = 3x^1/2

f^-1(x) = x²/9   or  1/9x²

300

Find f^-1(x)

f(x) = x^1/2 + 2

f^-1(x) = x² - 4x + 4

400

Find f^-1(2)  if f(x) = (8x)^1/2

1/2  or 0.5

Exponential Functions

100

Find the inverse.

f(x) = 5^x

f^-1(x) = log₅(x)

200

Find the inverse.

f(x) = 10^x - 1

f^-1(x) = log(x+1)

300

Find the inverse.

f(x) = e^x-4

f^-1(x) = ln(x) + 4

400

Find f^-1(36) if f(x) = 6^x

2

Logarithmic Functions

100

Find the inverse.

f(x) = log₂(x)

f^-1(x) = 2^x

200

Find the inverse.

f(x) = ln(x)

f^-1(x) = e^x

300

Find f^-1(10) if f(x) = 5log(x)

100

400

Find f^-1(x) if f(x) = ln(25x³) - ln(5x²)

f^-1(x) = 1/5e^x