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Chapter 5: Q. 12. (page 352)

For the function gx=3x+2.

: (a) Graph g using transformations. State the domain, range, and horizontal asymptote of g.

(b) Determine the inverse of g. State the domain, range, and vertical asymptote of g-1.

(c) On the same graph as g, graph g-1.

Short Answer

Expert verified

The graph is

The inverse of g is g-1x=log3x-2.

Domain of g = range of g-1=-鈭�,鈭�.

Range of g = domain ofg-1=2,鈭�.

Step by step solution

01

Step 1. Given Information.

The given function is

gx=3x+2.

02

Step 2.  Inverse of g .

We know that

gx=3x+2x=3x+2x-2=3xlogx-2=log3xx=log3x-2g-1x=log3x-2.

The domain of g-1= range of g =2,鈭�.

The domain of g = range ofg-1=-鈭�,鈭�.

03

Step 3. Graphing Utility.

The graph is

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