Relation & Functions
Question
Q1.
If f(x) = log x , f(y) = log y , find the value of f( x.y) .
(a) f(x) + f(y)
(b) f(x)
(c) f(y)
(d) 1
Solution.a
f(x.y) = log (x.y) = log x + log y = f(x) + f(y)
Solution
Q2.
The domain of {(2,1) (3,4) (6,9)} .
(a) (1)
(b) (2,3,6)
(c) (1,4,9)
(d) (1,3,9)
Solution. b
Note : First value in ordered pair is known as domain . (x,y) , x = Domain , y = Range
Solution
Q3.
If f(1) = 2 , f(4) = 8 , f(3) = 6 , find the domain of g , where g is the inverse of f .
(a) (6)
(b) (1)
(c) (2,8,6)
(d) (1,4,3)
Solution. c
f : (1,4,3) → (2,8,6)
∴ f : A → B (A = Domain , B = Range)
So in f-1 = g : (2,8,6) → (1,4,3)
Solution
Q4.
If f(x) = x + 3 , g(x) = x², then fog(x) .
(a) x + 3
(b) 3
(c) x²
(d) x² + 3
Solution. d
fog(x) = f[g(x)] = f(x²) = x² + 3
Solution
Q5.
If f(x) = log x , then f(
x/y
) will be
.
(a) f(x) - f(y)
(b) f(x)
(c) f(y)
(d) f(x) + f(y)
Solution. a
f(
x/y
) = log
(
x/y
) = log x - log y =
f(x) - f(y)
Solution
