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

Step 1

*Known Fact*:

__Procedure for finding the inverse of a one-to-one function__:

- Replace
*f(x)*with*y*. - Interchange
*x*and*y*. - 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*.

Step 3

Further simplif...

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