All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
JEE Exam  >  JEE Questions  >  The function h is defined by h(x)= under root... Start Learning for Free
SaveJoin the Discussion on the App
The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45?
Clear all your JEE doubts with EduRev
Most Upvoted Answer
The function h is defined by h(x)= under root x^2 -1 for x less that o...
1.) Geometrical relationship between the graphs of y=h(x) and y=h^-1(x):
The function h(x) represents a downward-opening parabola that is defined for x ≤ -1. The graph of h(x) will have two branches: one for x ≤ -1 and another for x > -1. The graph will be symmetric about the y-axis.

The function h^-1(x) represents the inverse function of h(x), which means it swaps the x and y coordinates of points on the graph of h(x). Since h(x) is a parabola, the inverse function will be a sideways-opening parabola. The graph of h^-1(x) will have two branches: one for x ≤ -1 and another for x > -1. The graph will be symmetric about the line y = x.

Therefore, the geometrical relationship between the graphs of y=h(x) and y=h^-1(x) is that they are reflections of each other across the line y = x.

2.) Expression for h^-1(x):
To find the expression for h^-1(x), we need to swap the x and y coordinates of points on the graph of h(x) and solve for y.

Let y = h(x)
Then, x = √(y^2 - 1)
Squaring both sides,
x^2 = y^2 - 1
Rearranging the equation,
y^2 = x^2 + 1
Taking the square root of both sides (considering the positive square root since y is a function),
y = √(x^2 + 1)

Therefore, the expression for h^-1(x) is y = √(x^2 + 1).

3.) Exact solution of gf(x) = 45:
Given that gf(x) = 45, we can substitute the expression for g(x) into the equation and solve for x.

g(x) = √(x^2 - 1)
gf(x) = √(f(x)^2 - 1)
45 = √(f(x)^2 - 1)

Squaring both sides to eliminate the square root,
2025 = f(x)^2 - 1
2026 = f(x)^2
Taking the square root of both sides (considering the positive square root since f(x) is a function),
f(x) = √2026

Therefore, the exact solution of gf(x) = 45 is f(x) = √2026.
Explore Courses for JEE exam

Similar JEE Doubts

Not differentiable then S 2019 won is an empty set to equals minus 2 minus 1 0 1 2 3 equals minus 2 minus 1 1 2 4 equals minus 2 2 ANS 2 solution FX is not differentiable at negative 2 minus 1 and 2 s equals minus 2 minus 1 0 1 2 qu 21 let F be a differentiable function such than FXX greater than 0 and F14 then 2019 1 exists and equals 4/7 2 exists and equals 4 3 does not exist 4 exists and equals 0 ANS 2 solutions reply equals FX solution of differential equation 22 let's denote the greatest integer less than or equal to 10 spend 2019 equals pi plus 1 11 equals 0 and 1 solution just since it does not exist You 23 2019-102 like four for one ANS 4 solution huge 24 let F equals RB differentiable at CR and F C equals 0 If GX equals FX then at X equals C G is 20191 not differentiable if FC equals 0 to differentiable if FC03 differentiable if FC equals 04 not differentiable ANS 3 solution Q25 is continuous at x equals 0 than the ordered pair PQ is equal to 2019 ANS 3 solution Q26 LED FRRB a continuously differentiable function such that F2 equals 6 and F2 equals 148 2019 1 18/24 3/12/436 ANS 1 solution Q27 2019/1424 square root 2 3/8 square root 248 A for solution Q28 2019 ANS 2 solution huge 29 if the function has to find on is continuous then K is equal to 2019 1 2 2 1 have 3 1 4 1 / square Benz FX is continuous then Q30 Let FX equals 15 minus X 10 X are then the set of all values of X at This is not differentiable is 2019-15 to 10 15 3 5 10 15 24 10 ANS 1 solution Since FX equals 15 minus 10X GX equals FFX equals 15 minus 10 minus 15 minus 10X equals 15 10X 5 then the points were function GX is non-differential or 10 X equals 0 and 10 X equals 5X equals 10 and X 10 equals plus minus 5 X equals 10 and X equals where it's denotes the greatest integer function then 2019 one F is continuous at X equals 4 ANI One solution Q32 if the function is continuous at x equals 5 then the value of A B is 2019 ANS 4 solution function is continuous at x equals 5 LHL equals RHL5 minus pi B plus 3 equals 5 minus pi A plus 1 Q3 and 1914 square root 22 square root 232 square root 244 ANS 1 solution Q34 let FRRB a differential function satisfying F3 plus F2 equals 0 then is equal to 2019 1 1 2 E 1 3 4 E2ANS 1 solution Q35 if FRR is a differentiable function and F2 equals 6 then 2019/124F222F230412F2 ANS 4 solution Using L hospital rule and Live NetSerum we get putting X = 2 2 F2 F2 = 12 F2 F2 = 6 Q36 2019/18/33 seconds 4/3 AMS One solution GX = FX + FX Then in the Interval - 2/2 G is one differentiable at all points two not continuous three not differentiable at two points four not differentiable at one point ANS 4 solution GX is non-differentiable at x equals 1 GX is not differentiable at one point Q38 let KB the set of all real values of x were the function fx = sin x minus x plus 2x minus pi cos x is not differentiable Then the set k is equal to 2019 empty set 2 pi 3 0 4 0 pi ANS 1 solution Then function f x is differentiable for l Related: JEE Main Previous year questions (2016-20): Limits, Continuity and Differentiability?

Top Courses for JEEView all

Top Courses for JEE

The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45?
Question Description
The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45?.
Solutions for The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45? defined & explained in the simplest way possible. Besides giving the explanation of The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45?, a detailed solution for The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45? has been provided alongside types of The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45? theory, EduRev gives you an ample number of questions to practice The function h is defined by h(x)= under root x^2 -1 for x less that or equal to -1. 1.) State the geometrical relationship between the graphs of y=h(x) and y=h^-1(x). 2.) Find an expression for h^-1(x). 3.) Find the exact solution of gf(x)=45? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup