EXERCISE - A
1) Given f(x)= 2x +3; x belongs to R
Find i) f(-2).
ii) find a if f(a)= -5
iii) Is f(x)= 2x+3, a function ? Give reason.
2) given f(x)=2x² -3 , x belongs to R
Find
i) f(0).
ii) f(-2).
iii) f(-a)+1
iv) 2f(4) - 1/2 f(-5) ?
3) Let f(x)= (3x-1)/(x - 3) , x≠3
Find i) f(-x)
ii) f(1/x)
iii) f(5)/f(0)
iv) f(-3)/f(1/3)
v) f(a/b) x f(b/a)
4) Given f(x)= x³-,find x if f(x) is 215
5) if f(x)= 2x+1 and g(x)= x² find
i) f(-3)
ii) g(-3)
iii) gf(-3)
iv) f g (-3)
6) Let be defined by f(x)=x/(x²+1) ,
x belongs to R. Find
i) f(1/x) , x≠0
ii) f(2x)
iii) f(x - 1)
iv) f[f(-1)]
v) f[f{f(1/x)}]
7) Let the function f: N -> N be defined by.f(x)= 2x -1,. If x is odd
x+2. If x is even
Find i) f(2)=
ii) f(1)
iii) f(17)
iv) f(2)+f(7)
v) 1/2. f(3) + f(5)
8) Let the function f: R -> R be
f(x)=. 2x +1 ,. If x > 2
x - 1,. If -3≤x≤2
3x+2,. If x < -3. Find
I) f(1)
ii) f(-4)
iii) f(-3) +f(3)
iv) f(6)/f(-2)
9) Given f(x)=4x²+1, where x belongs to Z
I) find domain and range of f
ii) find f(1)
iii) find the elements of domain whose images are 101
iv) find x, if f(x)=37
10) A function f is defined by
f x -> 3x+1, x belongs to W.
List the elements of f for which
x <4 and find the corresponding elements of range.
11) A function f is defined on the set real numbers as follows:
f(x)=. 1+x ; 1≤x2
2x-1 ; 2≤x<4
3x -10; 4≤x<6. Find
I) the domain of the function
ii) range of the function
iii) value of f(4)
12) If f(x)=(x²-5x+6)/(x²-8x+12) then find
a) f(2) b)f(-5) c) f(0)
d) f(h+1) e) f(2+h) f) f(2/h)
13) If f(x)=2x²-5x+4 then finf
a) f(2x) b) 2f(x)
c) if f(2x) = 2f(x) then find the value
of x.
14) If f(x) = (x-a)(x-b)(x-c) find
a)f(a) b) f(c) c) f(0)
15) If f(x) =(ax+b)/(bx+a) find
f(x).f(1/x)
16) Let y=f(x)=(x+1)/(x+2) find
a) f(y) b) f(1/x) c) f{f(1/x)}
6) If f(x)=10x²-13x+13 find the
value of x when f(x)=16
17) if f(x) = (x-1)/(x+1) find the value of {f(x)+f(y)}/{1+f(x).f(y)}
18) If y=f(x)=(ax+b)/(bx-a) find f(y)
19) if f(x) = (4x-5)/(3x-4) find f{f(x)}
20) Given f(x) = x+a and g(x)=x-a
find the value of {f(x)}² - {g(x)}²
21) If y= f(x)=(x+3)/(2x+1) and
z=f(y) Express z=f(x).
22) Given g(x) = (x-a)/x + x/(x-b)
find the value of g(a+b)/2.
23) If f(x) = 1/x² find f(x+h)-f(x-h)
24) If f(x-1)=7x-5 find f(x+2)
25) If f(x)=x/(1-x) find
{f(x+h)-f(x)}/h.
26) If f(2x-1) = (x+1)/(x+2) then
find
a)f(x) b) f(0) f(h+1) c) f(2+h)
27) f{(x-2)/(x+3)} =(x-1)/(2x+1)
find the value of f(5-2x)
28) If f(x) = (5)ˣ find
a) f(x+2)
b) f(x+y)
c) f{(2x+1)/(x+2)}
d) f(log₅x)
29) If f(x) = eᵖˣ⁺ᵗ
find {f(a)f(b)f(c)}/f(a+b+c)
30) If f(x) =
a{(x-b)/a-b)} +b{(x-a)/(b-a)}
find the value of f(a)+f(b)
31) if f(x) = 2x²+1 and x≼2
1/(x-2) and 2≺x≼3
2x -5 and x ≻ 3
find the value of
a)f(0)
b) f√(2)
c) f(-2)
d) f(4)
e) f(2.5)
32) eʸ +e⁻ʸ = 2x find y
33) Given f(x)=ax²+bx+c and
f(1)=3 , f(2)=7,f(3)=13 find a, b, c.
34) if f(x)=a/x +b/x +cx and
f(1)=5,f(-2)=2,f(-1)=-3,find f(-3)
35) if f(x+3)=2x²-3x-1 findf(x+1)
36) if f(x+3)=3x²-2x+5 find f(x-1)
37) find even and odd or neither
even nor odd of the following.
a) f(x)=x²+x⁴+x⁶
b) f(x) = 4ˣ +4⁻ˣ
c) f(x) = c
d) f(x) = x(3ˣ +1)/(3ˣ - 1)
d) f(x) = x+x³+x⁷
e) f(x) = 3x³ +x
f) f(x) = (2ˣ+1)/(2ˣ - 1)
g) f(x)= log(x+√(x²+1)).
38) Which of the following Relation are function ? Give your reasons. In case of function, determine its domain and range.
a) {(1,-2),(3,7),(4,-6),(8,11)}
b) {(1,0),(1,-1),(2,3),(4,10)}
c) {(a,b),(b,c),(c,b),(d,c)}
d) {(2,3),(1,4),(2,1),(3,2),(4,4)}
e) {(3,1),(4,2),(1,1)}
f) {(1,2),(2,2),(3,2),(4,2)}
g) {(x,y): x belongs to A, y belongs to B is surname of x} where A is the set of people in India and B is the set of surnames.
h) {(x,y): x belongs to A, y belongs to B, y is the area of a square of sidex} where A is the set of measurement of length.
i) {(x,y): x belongs to B, y belongs to P, y is a passenger on X} where B is the set of buses of a school and P is the set of pupils of some schools.
j) y= 3x+2
k) a is the capital of b where b belongs to B and B is the set all countries, a belongs to A and A is the set of capital cities of countries.
l) y< x+3.
m) y is Math teacher of x where x represents any pupil taking up Maths in a school.
n) y is Maths pupil of x, where x represents any Maths teacher in a school.
39)State the domain of following:
a) f : -> 5x
b) g : ->5x, x belongs to Z
c) h : x -> 2/(x -7)
d) F: x -> 5x, x belongs {0,1,2}
e) f: x -> x/5
f) F: x -> 6/x
g) H: x -> x²+5x-6
h) g: x -> (x -4)/{(x-3)(x+6)}
i) g: x -> x/1, x belongs to {2,4,6}
j) g: x -> 1/x, x belongs to R
40) Find whether the function are one-on-one or not.
a) f: R ->R, defined by f(x)=x³, x belongs to R.
b) f: Z -> Z, defined by f(x)=x²+5, x belongs to Z.
c) f: R {3} ->R, defined by
f(x)=(5x+7)/(x - 3), x belongs to R-{3}
d) f: R -> R, defined by f(x)= |x|, x belongs to R.
e) f: {(2,7),(3,4),(7,9),(-1,6),(0,2),(5,3)
Is it a function, if yes it is one-one or not.
Interchange the order to find the same.
f) To each person on the earth assign the number which corresponds to his age.
g) To each country in the world assign the latitude and longitude of its capital.
h) To each book written by only one author assign the author.
i) To each country in the world which has a prime minister assign its prime minister.
41) Find whether the following are onto functions (surjections) or not.
a) f: R ->R, defined by f(x)=x³+5 for x belongs to R.
b) f: R -> R, defined by f(x)=x²+3, x belongs to R.
c) f: Z -> Z, defined by f(x)= 5x - 9, x belongs to Z.
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