Consider the function f defined by f(x) = 90 -0.5* for x = R*. The graph of ƒ and the line y=x intersect at point P. (a) Find the x-coordinate of P. The line I has a gradient of -1 and is a tangent to the graph of ƒ at the point Q. (b) Find the exact coordinates of Q. (c) Show that the equation of I is y = -x+21n45 +2. The shaded region A is enclosed by the graph of ƒ and the lines y = x and L. (d) (i) y=x Find the x-coordinate of the point where I intersects the line y = x. (ii) Hence, find the area of 4. The line I is tangent to the graphs of both f and the inverse function f¹. x (e) Find the shaded area enclosed by the graphs of f and f-¹ and the line L.

Consider the function f defined by f(x) = 90 -0.5* for x = R*. The graph of ƒ and the line y=x intersect at point P. (a) Find the x-coordinate of P. The line I has a gradient of -1 and is a tangent to the graph of ƒ at the point Q. (b) Find the exact coordinates of Q. (c) Show that the equation of I is y = -x+21n45 +2. The shaded region A is enclosed by the graph of ƒ and the lines y = x and L. (d) (i) y=x Find the x-coordinate of the point where I intersects the line y = x. (ii) Hence, find the area of 4. The line I is tangent to the graphs of both f and the inverse function f¹. x (e) Find the shaded area enclosed by the graphs of f and f-¹ and the line L.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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