Question
Asked Feb 20, 2019
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The function f(x) = 9/4+x is one to one
a. Find its inverse and check your answer
b. Find the domain and the range of f and f^-1

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Expert Answer

Step 1

Known Fact:

Procedure for finding the inverse of a one-to-one function:

  1. Replace f(x) with y.
  2. Interchange x and y.
  3. Solve this equation for y. The resulting equation is f^-1 (x).

Domain and range of f and f ^-1:

The inverse function interchanges the domain and range. Namely, Domain of f = Range of f ^-1 Range of f = Domain of f ^−1.

Property of inverse functions:

Let f be a one-to-one function with domain A and range B. The inverse function f ^1 satisfies f ^-1 (f(x)) = x for every x in A and f(f ^-1 (x)) = x for every x in B.

Step 2

Calculation:

a.

Use the above procedure and obtain the inverse of the function f(x) =9/4+x.

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Step 3

Further simplif...

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