The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

(Marvins-Underground-K-12) #1
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WORKSHEET 8.10: FINDING THE INVERSE OF A FUNCTION
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The inverse of a functionf(x)is denoted asf−^1 (x). To find the inverse of a function, follow the
steps below:


  1. Express the function as an equation,y=an expression.

  2. Replaceywithxandxwithy.

  3. Solve the equation fory.

  4. Rewrite the equation, replacingywithf−^1 (x).


EXAMPLES
Find the inverse of each function.

f(x)= 2 xg(x)=x^3 + 9

y= 2 xy=x^3 + 9

x= 2 y Switchxandy. x=y^3 + 9

2
x
=y Solve fory. x− 9 =y^3

x
2
=f−^1 (x)^3


x− 9 =y

√ (^3) x− 9 =g− (^1) (x)
DIRECTIONS: Find the inverse of each function.



  1. f(x)= 7 x 2. g(x)=− 4 x 3. h(x)=x^3

  2. I(x)= 3 x− 10 5. F(x)= 2 x^3 − 9 6. k(x)=x+ 2


CHALLENGE:Jeffrey said thatf(x)=x^2 has an inverse off−^1 (x)=±


x,which
is also a function. Is he correct? Explain your answer.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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