Inverse, Exponential, and Logarithmic Functions

Problem : Find the inverse of f (x) = .

Solution for Problem 1 >>

y =

Solve for x first:

(x - 1)y		= x + 2
xy - y		= x + 2
xy - x		= y + 2
x		=

Now switch the variables x and y :

y =

Close

Problem : Find the inverse of f (x) = 6 + 5x ³ .

Solution for Problem 2 >>

y		= 6 + 5x 3
x		=

Now switch variables:

y =

Close

Problem : If f (3) = 2 and f'(3) = 7 , what is (f ^-1)'(2) ?

Solution for Problem 3 >>

(f ^-1)(2) = , since the slope of the inverse is the reciprocal.

Close

Problem : Find (f ^-1)'(2) for f (x) = 4x ³ - 2x + 2 .

Solution for Problem 4 >>

Note that f is not one-to-one throughout its domain, so it does not have an inverse defined on its entire range. However, there is a unique x , namely 0, such that f (x) = 2 . So, for a suitable domain containing 0, the inverse can be defined, and we may compute:

(f -1)'(2)		=
		=
		= -

Close

Problem : Find (f ^-1)'(- 4) for f (x) = x ³ - x ² - 4x .