Name Date
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:
- Express the function as an equation,y=an expression.
- Replaceywithxandxwithy.
- Solve the equation fory.
- 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.
- f(x)= 7 x 2. g(x)=− 4 x 3. h(x)=x^3
- 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.