Finding Inverses of Exponential and Logarithmic Functions

Find the inverse of the equation

• 2^(x-9)+5=y
• 2^(x+9)-5=y
• 5^(x-9)-5=y

Find the inverse of the equation

• y=2^(x+9)-5
• y=2^(x-9)-5
• y=2^(x+9)+5
• y=2^(x+5)-9

When finding the inverse of a relation, 
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

• solve for y
• replace y with f^-1(x)
• solve for x
• find the greatest common factor

Convert to exponential form. log₄ (4) = x

• log_x (4) = 4

• x⁴ = 4

• 4^x = 4

• log₄ (x) = 4

Convert to exponential form. log_x (y) = z

• x^z = y

• z^x = y

• y^z = x

• z^y = x

Find the inverse of

• f(x) = 4^x/2+9

• f(x) = 4^(x+9)/2

• f(x) = 4^(2x+9)

• f(x) = 4^(2x)+9

Find the inverse of the function:
f(x) = 10^3x

• f^-1(x)=log(3x) 
• f^-1(x)=3log(x) 
• f^-1(x)=⅓ log(x)
• f^-1(x)=⅓ ln(x)

Find the inverse of y=5^x-8

• y=log₅(x-8)
• y=log₅(x+8)
• y=log₈(x-5)
• y=log₈(x+5)

Find the inverse of
f(x) = 3^x-1 + 9

• log₃(x-9) = f^-1(x)
  
• log₃(x)-8 = f^-1(x)
• log₃(x-9)+1 = f^-1(x)
• log₃(x+9) -1 = f^-1(x)

Find the inverse

• A

• B

• C

• D