`[0, pi]` and `[-1, 1]`
`[-pi/2 , pi/2]` and `[-1 , 1]`
`[0 , pi]` and `(-1 , 1)`
`[0, pi]` and `[0, 1]`
`f(- a/(a+1))`
`f(a^2)`
`f(1/a)`
`f(-a)`
`(p) = g(m)`
`(q) = g(n)`
`f(n) = g(q)`
`f(m) = g(p)`
one-one and into
neither one-one nor onto
many-one and onto
one-one and onto
`x^2-1`
`x+ 3/x`
`|x|`
`x^2 (x-3)`
1 only
2 only
Both 1 and 2
Neither 1 nor 2
ln `( (1 - x)/(1+x))`
ln `( (2 + x)/(1 - x))`
`tan^(-1) ( (1 - x)/(1+x))`
`tan^(-1) ( (1 + x)/(1 - x))`
`[0, 1)`
`[0, 1]`
`(0, 1)`
`(0, 1]`
At `(2, 3)` only
At `(-1,- 2)` only
At `(2, 3)` and `(-1,- 2)`
Neither at `(2, 3)` nor at `(-1,- 2)`
One
Two
Three
Four
`(-oo , 0)`
`(0 , oo)`
`0 < x < 1`
`x > 1`
`-2`
`-1`
`0`
`4`
`-1`
`0`
`1`
`2`
`-1`
`0`
`1`
`2`
`[0 ,oo)`
`(-oo, 0)`
`[1,oo)`
`(- oo, 0]`
`f(f(f(g(g(f(x)))))) = g(g(f(g(f(x)))))`
`f(g(g(g(f(x))))) = g(g(f(g(f(x)))))`
`f(g(f(g(g(f(g(x))))))) = g(g(f(g(f(x)))))`
`f(f(f(g(g(f(x)))))) = f(f(f(g(f(x)))))`
a null set
a set consisting of only one element
a set consisting of two elements
a set consisting of infinitely many elements
`2`
`1`
`0`
`1/2`
I and II
II and III
I and III
I, II and III
`( (x+7)/3 ) ^(1//3)`
`( (x-7)/2 ) ^(1//3)`
`( x- 7/2 ) ^(1//3)`
`( x + 7/2 ) ^(1//3)`
Both the statements are true and Statement II is the correct explanation of Statement I
Both the statements are true and Statement II is not the correct explanation of Statement I
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.
polynomial functions f
trigonometric functions f
exponential functions f
logarithmic functions f
injective and surjective
injective but not surjective
not injective but surjective
neither injective nor surjective
`f(c) = g(a)`
`f(a) = g(c)`
`f(c) = g(d)`
`f(d) = g(b)`
one-one but not onto
onto but not one-one
Both one-one and onto
Neither one-one nor onto
`0`
`1`
`2x`
`4x`
`(f(x) + 1)/(f(x) + 3)`
`(f(x) + 1)/(3f(x) + 1)`
`(3f(x) + 1)/(f(x) + 3)`
`(f(x) + 3)/(3f(x) + 1)`
`x`
`- x`
` - 1/x`
None of these
Set of all real numbers
Set of all integers
`{-1,1}`
`{ -1 ' 0, 1}`
one to one but not onto
onto but not one-one
Both one-one and onto
Neither one-one nor onto
`f` is one-one and onto
`f` is one-one but not onto
`f` is only onto
`f` is neither one-one nor onto
t + k
`ct + k`
`t^k + c`
`t^k`
`f(x) = 3x + 5`
`f(x) = 3x - 5`
`f(x) = 5x- 3`
`f(x)` does not exist
`[2, 4]`
`[- 1, 1]`
`[- sqrt(2), sqrt(2)]`
`(- sqrt(2), 2)`
`-1` ana `1`
`-2` and `2`
`-sqrt2` and `sqrt 2`
None of these
`3/2 x+2/3`
`3/2 x-9/2`
`2/3 x-4/9`
`2/3 x -2/3`
`-9`
`0`
`9`
`3`
Only I
Only II
Both I and II
Neither I nor II
The function is one-one into
The function is many-one into
The function is one-one onto
The function is many-one onto
onto but not one-one
one-one onto
one-one but not onto
Neither one-one nor onto
one-one as well as onto
onto but not one-one
Neither one-one nor onto
one-one but not onto
`{1,2}`
`{1,-1}`
`{-1,1,2}`
`{1}`
one-one only
onto only
one-one onto
Neither one-one nor onto
`f(x) = | x | , AA x in R`
`f(x) = x^2, AA x in R`
`f(x) = 11, AA x in R`
`f(x) = - x , AA x in R`
f is one-one but not onto
f is onto but not one-one
f is both one-one and onto
f is neither one-one nor onto
Only I
Only II
Both I and II
Neither I nor II
`0 , AA x in R`
`2x, AA x in R`
`{tt((2x, for x ge 0),(0, for x < 0))`
`{tt((0, for x ge 0),(2x, for x < 0))`
`1`
`1/(sin(sin x))`
`1/(sin^2 x)`
`sin(1/(sin x))`