Determine the inverse function f ( x ), Mathematics

Assignment Help:

Given f ( x ) = 3x - 2 determine     f -1 ( x ) .

Solution

Now, already we know what the inverse to this function is as already we've done some work with it.  Though, it would be nice to in fact start with this as we know what we have to get. This will work as a nice verification of the procedure.

Hence, let's get started. We'll replace first f ( x ) with y.

                                                    y = 3x - 2

Next, replace all of the x's along with y and all y's with x.

                                                     x = 3 y - 2

Now, solve out for y.

x + 2 = 3 y

1/3 ( x + 2) = y

Lastly replace y with f -1 ( x ) .

f -1 (x)= x/3 + 2/3

Now, we have to verify the results.  Already we took care of this in the previous section, though; really we have to follow the procedure so we'll do that here. It doesn't matter which one from two that we verify we just have to check one of them.  This time we'll check that ( f o f -1 )( x ) = x is true.

 ( f o f -1 )( x ) = f [ f -1 ( x )]

                        =f [ x/3 + 2/3 ]

                        = 3 ( x /3+ 2 /3) - 2

                            = x +2 - 2

                         = x


Related Discussions:- Determine the inverse function f ( x )

Integer exponents, We will begin this chapter by looking at integer exponen...

We will begin this chapter by looking at integer exponents.  Actually, initially we will suppose that the exponents are +ve as well. We will look at zero & negative exponents in a

Determine the length of the field, A rectangular field is to be fenced in c...

A rectangular field is to be fenced in completely. The width is given as 22 yd and the total area is 990 yd 2 . Determine the length of the field? a. 31 yd b. 45 yd c. 968

Geometry , solve for x and y 2x+3y=12 and 30x+11y=112

solve for x and y 2x+3y=12 and 30x+11y=112

Word problems, if I read 6 hours of spring break how many minutes did ...

if I read 6 hours of spring break how many minutes did read

Word problem, A girl has 25 plants in all, 8 of them are tomatos. She has 1...

A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?

Find the constant rate of 0.01 , Two people are 50 feet separately.  One of...

Two people are 50 feet separately.  One of them begin walking north at rate so that the angle illustrated in the diagram below is changing at constant rate of 0.01 rad/min. At what

Product rule, Product Rule If the two functions f(x) & g(x) are differe...

Product Rule If the two functions f(x) & g(x) are differentiable (i.e. the derivative exist) then the product is differentiable and,

Definition of the laplace transform, Definition Assume that f(t) is a ...

Definition Assume that f(t) is a piecewise continuous function. The Laplace transform of f(t) is denoted L{ f (t )} and defined by, There is an optional notation for L

Logarithms, find any integer from 1-128 on a logarithmic scale

find any integer from 1-128 on a logarithmic scale

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd