CK-12-Pre-Calculus Concepts

10.4. Parametric Inverses http://www.ck12.org

Example B
Is the point (4, 8) in the following function or its inverse?

x= 2 t^2 − 2

y=t^2 − 1

Solution:Try to solve for a matchingtin the original function.

TABLE10.1:

x= 2 t^2 − 2

4 = 2 t^2 − 2

6 = 2 t^2

3 =t^2

±

√

3 =t

y=t^2 − 1

8 =t^2 − 1

9 =t^2

± 3 =t

The point does not satisfy the original function. Check to see if it satisfies the inverse.

TABLE10.2:

x=t^2 − 1

4 =t^2 − 1

±

√

5 =t

y= 2 t^2 − 2

8 = 2 t^2 − 2

10 = 2 t^2

±

√

5 =t

The point does satisfy the inverse of the function.
Example C
Parameterize the following function and then graph the function and its inverse.
f(x) =x^2 +x− 4
Solution:For the original function, the parameterization is: