A function f has the tangent line y=2x+1 at the point (3,7). Find the equation of tangent line of f^-1 at the point (7,3) in slope-intercept form.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
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A function f has the tangent line y=2x+1 at the point (3,7). Find the equation of tangent line of f^-1 at the point (7,3) in slope-intercept form.

Expert Solution
Step 1

Given data:

 

 

The given expression for the function is: y=2x+1.

The given point is: (x1,y1)=(7,3).

 

 

The expression for the inverse function is,

Calculus homework question answer, step 1, image 1

Replace y by x in the above expression.

Calculus homework question answer, step 1, image 2

Step 2

The expression for the slope of the above expression is,

Calculus homework question answer, step 2, image 1

Substitute the above-calculated value in the expression.

Calculus homework question answer, step 2, image 2

 

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