I and II
II and III
I and III
All of these
one - one and into
many-one and into
one-one and onto
many - one and onto
`( - oo , log_e (11)/3 ]`
`[ log_e (11)/3 , oo)`
`[ - log_e (11)/3 , log_e (11)/3]`
None of these
`[ 1/3 , 1 [`
`[ 1/3 , 1 ]`
`[ 1/3 , 1 [`
`[ 1 , 1/3 ]`
`] - 3 , - 2 .5 [ cup ] - 2.5 - 2 [`
`[-2 , 0 [ cup] 0 , 1 [`
`] 0 ,1 [`
None of these
`R`
`( - oo , 1)`
`(1, oo)`
`(2/3 , oo)`
`0`
`-1`
`1/4`
`- 1/8`
1 only
2 only
Both 1 and 2
Neither 1 nor 2
`f(x_1 ) · f(x_2 ) = f(x_1 + x_2)`
`f(x + 2)- 2f(x + 1) + f(x) = 0`
`f(x) + f(x + 1) = f(x2 + x)`
`f(x_1) + f(x_2) = f ((x_1+x_2)/(1+x_1x_2))`
`(-oo,(-1)/3) cup (1/4,oo)`
`(-oo,(02)/3) cup [5/4,oo)`
`(-oo,(-1/3)) cup [2,oo)`
`(-oo, -2/3] cup[4,oo)`
` (x^2 + 2x - 1)/6`
` (x^2 + 2x - 1)/3`
` (x^2 + 4x - 1)/3`
` (x^2 + 4x - 1)/6`
`[3/5,5/3]`
`(3/5,5/3)`
`(-oo, 3/5) cup (5/3 , oo )`
`[-5/3 , -3/5]`
`log_10 (2-x)`
`1/2 log_10 ((1+x)/(1-x))`
`1/2 log_10 (2x-1)`
`1/4 log_10 (2x)/(2-x)`
`(x^2 - y^2)/8`
`(x^2 - y^2)/4`
`(x^2 + y^2)/4`
`(x^2 -y^2)/2`
`0`
`1//2`
`1`
`2`
` ( (x - 7)/3)^(1//2)`
` ( (x + 7)/3)^(1//2)`
` ( (x - 3)/7)^(1//2)`
` ( (x + 3)/7)^(1//2)`
range of `f` is `{ -1 ,1 }`
`f` is an even function
`f` is an odd function
`f` is one - one function
an even function
an odd function
periodic function
None of these