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 )

Draw grouped frequency tables, Q. Draw Grouped Frequency Tables? Ans. ...

Q. Draw Grouped Frequency Tables? Ans. Grouped frequency tables are often used when there are many different values. In these tables, the values are grouped into classes

Logarithmic functions- general properties, Logarithmic functi...

Logarithmic functions have the following general properties If y = log a x, a > 0 and a ≠1, then The domain of the function

Prove the arithmetic progressions equation, Prove that a m + n + a m - n ...

Prove that a m + n + a m - n  =2a m Ans:    a m + n = a 1 + (m + n - 1) d a m-n = a 1 + (m - n -1) d a m = a 1 + (m-1) d Add 1 & 2 a m+n + a m-n  =

Fractions, question paper on fractions

question paper on fractions

Alcohol solution (mixture), Nora works at a laboratory as a chemist . she w...

Nora works at a laboratory as a chemist . she was told to prepare 100L of 25% alcohol solution. she has on hand of a 15% percent alcohol solution and a 40% alcohol solution which s

Mdm4uc, The number of hours spent studying and achievement on an exam

The number of hours spent studying and achievement on an exam

Setofoperations, write CxD being sure to use appropriate brackets and find ...

write CxD being sure to use appropriate brackets and find n(CxD)

Least common denominator of rational expression, Perform the denoted operat...

Perform the denoted operation.                    (4/6x 2 )-(1/3x 5 )+(5/2x 3 ) Solution For this problem there are coefficients on each of term in the denominator thus

Complex number, a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.fi...

a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k

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