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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Attached exercise componed by 2 parts: P1 and P2 (in this order to answer).
Please be cleared to explain all your steps.
Thanks ASAP
Transcribed Image Text: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.
Transcribed Image Text: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.
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