Question
The image of the interval [- 1, 3] under the mapping specified by the function 
is :
- [f(+1), f(-1)]
- [f(-1), f(3)]
- [- 8, 16]
- [-8, 72]
The correct answer is: [-8, 72]
we are asked to find the image of the interval under the mapping specified by the function
we need to differentiate the function to get local maxima/minima
f′(x)=12(x2−1)
f′(x)=0 at x=±1
f′(x)<0 If ∣x∣<1
function will be increasing in this range (∣x∣<1 )
f′(x)>0 If ∣x∣>1
function will be increasing in this range (∣x∣>1 )
f(x) is min when x=1
f(1)=−8
f(x) is max either at x=−1 or x=3
f(−1)=8 , f(3)=72
So image [-8, 72] in [-1, 3]
f′(x)=12(x2−1)
f′(x)=0 at x=±1
f′(x)<0 If ∣x∣<1
f′(x)>0 If ∣x∣>1
f(x) is min when x=1
f(1)=−8
f(x) is max either at x=−1 or x=3
f(−1)=8 , f(3)=72
So image [-8, 72] in [-1, 3]
Hence the correct option in [-8,72]
Related Questions to study
Let f(x)
defined from 
, then by f(x) is -
Let f(x) defined from , then by f(x) is -
If f : R 
R is a function defined by f(x) = [x] 
, where [x] denotes the greatest integer function, then f is :
The correct answer is choice 2
If f : R R is a function defined by f(x) = [x] , where [x] denotes the greatest integer function, then f is :
The correct answer is choice 2
Let ƒ : (–1, 1) B, be a function defined by ƒ(x) 
then ƒ is both one-one and onto when B is the interval-
Hence, the range of the given function is 
.
Let ƒ : (–1, 1) B, be a function defined by ƒ(x) then ƒ is both one-one and onto when B is the interval-
Hence, the range of the given function is .
The range of the function 
is-
Hence, range of the given function will be R−{−1}
The range of the function is-
Hence, range of the given function will be R−{−1}
A function whose graph is symmetrical about the origin is given by -
Hence, the function f(x+y)=f(x)+f(y) is symmetric about the origin.
A function whose graph is symmetrical about the origin is given by -
Hence, the function f(x+y)=f(x)+f(y) is symmetric about the origin.
The minimum value of 
is
The minimum value of is
is -
Hence, the given function is many one and onto.
is -
Hence, the given function is many one and onto.
If f(x) is a polynomial function satisfying the condition f(x). f(1/x) = f(x) + f(1/x) and f(2) = 9 then -
If f(x) is a polynomial function satisfying the condition f(x). f(1/x) = f(x) + f(1/x) and f(2) = 9 then -
Fill in the blank with the appropriate transition.
The movie managed to fetch decent collections ______ all the negative reviews it received.
Fill in the blank with the appropriate transition.
The movie managed to fetch decent collections ______ all the negative reviews it received.
If R be a relation '<' from A = {1, 2, 3, 4} to B = {1, 3, 5} i.e. (a, b) 
R iff a < b, then 
is 
Values of are {(3, 3), (3, 5), (5, 3), (5, 5)}
If R be a relation '<' from A = {1, 2, 3, 4} to B = {1, 3, 5} i.e. (a, b) R iff a < b, then is
Values of are {(3, 3), (3, 5), (5, 3), (5, 5)}
Which one of the following relations on R is equivalence relation
Which one of the following relations on R is equivalence relation
Let R = {(x, y) : x, y A, x + y = 5} where A = {1, 2, 3, 4, 5} then
Hence, the given relation is not reflexive, symmetric and not transitive
Let R = {(x, y) : x, y A, x + y = 5} where A = {1, 2, 3, 4, 5} then
Hence, the given relation is not reflexive, symmetric and not transitive
Let 
be a relation defined by 
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Hence, the given relation is Reflexive, transitive but not symmetric.
Let be a relation defined by Then R is
Hence, the given relation is Reflexive, transitive but not symmetric.
The relation R defined in N as aRb 
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Hence, the given relations is reflexive but not symmetric.
The relation R defined in N as aRb b is divisible by a is
Hence, the given relations is reflexive but not symmetric.
