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Common Inverse Functions

Table 2.4.1 shows some familiar functions which do have inverses. Note that in each case, 02_differentiation-212.gif.

Table 2.4.1

function
y = f(x)

02_differentiation-213.gif

inverse function
x = g(y)

02_differentiation-214.gif

y = x + c

1

x = y - c

1

y = kx

k

x = y/k

1/k

y = x2, x > 0

2x

x = √y

02_differentiation-215.gif

y = x2, x ≤ 0

2x

-x = -√y

02_differentiation-216.gif

y = 1/x

02_differentiation-217.gif

x = 1/y

02_differentiation-218.gif

Suppose the (x, y) plane is flipped over about the diagonal line y = x. This will make the x- and y-axes change places, forming the (y, x) plane. If f has an inverse function g, the graph of the function y = f(x) will become the graph of the inverse function x = g(y) in the (y, x) plane, as shown in Figure 2.4.5.

02_differentiation-223.gif

Figure 2.4.5
Home Differentiation Inverse Functions Common Inverse Functions

Last Update: 2006-11-05