5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

62 STEP 4. Review the Knowledge You Need to Score High

[−10, 10] by [10, 10]

Figure 5.3-6

(b) By inspection, the graph of f(x)=x^3 − 2 x+1 in Figure 5.3-7 fails the horizontal line

test. Thus,f(x) has no inverse function.

[−8, 8] by [−4, 3]

Figure 5.3-7

Example 3

Find the inverse function off(x)=

√

2 x− 1 .(See Figure 5.3-8.)

y = x

f

f−^1

y

0 x

0.5

0.5

Figure 5.3-8

1. Sincef(x) is a strictly increasing function, the inverse function exists.


2. Lety= f(x).Thus,y=

√

2 x−1.

3. Interchangexandy.You havex=

√

2 y−1.