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Lesson: Inverses of Exponential Functions

Sample Question Videos

Worksheet • 4 Questions • 2 Videos

Q1:

The function 𝑓 ( π‘₯ ) = 2 𝑒 + 3 π‘₯ has an inverse of the form 𝑔 ( π‘₯ ) = ( π‘Ž π‘₯ + 𝑏 ) l n . What are the values of π‘Ž and 𝑏 ?

  • A π‘Ž = 1 2 , 𝑏 = βˆ’ 3 2
  • B π‘Ž = 1 2 , 𝑏 = 3 2
  • C π‘Ž = 1 , 𝑏 = βˆ’ 3
  • D π‘Ž = 2 , 𝑏 = 3
  • E π‘Ž = βˆ’ 3 2 , 𝑏 = 1 2

Q2:

Make π‘₯ the subject of the equation 𝑦 = 2 π‘Ž π‘₯ + 𝑏 , assuming that π‘Ž β‰  0 .

  • A π‘₯ = ( 𝑦 ) βˆ’ 𝑏 π‘Ž l o g 2
  • B 𝑦 = ( π‘₯ ) βˆ’ 𝑏 π‘Ž l o g 2
  • C π‘₯ = ( 𝑦 ) βˆ’ 𝑏 l o g 2
  • D π‘₯ = ( 𝑦 βˆ’ 2 ) βˆ’ 𝑏 π‘Ž l o g
  • E π‘₯ = ( 𝑦 ) + 𝑏 π‘Ž l o g 2

Q3:

Rearrange the equation 𝑦 = 2 βˆ’ 1 2 + 1 π‘₯ + 1 π‘₯ to find π‘₯ in terms of 𝑦 . Hence determine the inverse 𝑔 βˆ’ 1 to the function 𝑔 ( π‘₯ ) = 2 βˆ’ 1 2 + 1 π‘₯ + 1 π‘₯ .

  • A 𝑔 ( π‘₯ ) = ο€Ό βˆ’ π‘₯ βˆ’ 1 π‘₯ βˆ’ 2  βˆ’ 1 2 l o g
  • B 𝑔 ( 𝑦 ) = ο€½ βˆ’ 𝑦 βˆ’ 1 𝑦 βˆ’ 2  βˆ’ 1 2 l o g
  • C 𝑔 ( π‘₯ ) = ο€Ό βˆ’ π‘₯ βˆ’ 1 π‘₯ βˆ’ 2  βˆ’ 1 l o g
  • D 𝑔 ( 𝑦 ) = ο€½ βˆ’ 𝑦 βˆ’ 1 𝑦 βˆ’ 2  βˆ’ 1 l o g
  • E 𝑔 ( π‘₯ ) = ο€Ό π‘₯ + 1 π‘₯ βˆ’ 2  βˆ’ 1 2 l o g

Q4:

Consider the function 𝑓 ( π‘₯ ) = 𝑏  , where 𝑏 is a positive real number not equal to 1. What is the domain of 𝑓 ( π‘₯ )   ?

  • A π‘₯ > 0
  • B π‘₯ > 𝑏
  • C all real numbers
  • D 0 < π‘₯ < 𝑏
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