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

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WORKSHEET 8.10: FINDING THE INVERSE OF A FUNCTION -------------------------------------------------------------------------------------

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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