To find questions from 1 to 4, please visit the page "Practice Worksheet Relations and Functions with Answers"
Question 5 :
Find the domain of the function f(x) =
Solution :
Let t = √(1 - √(1 - x2))
f(x) = √(1 - t)
1 - t ≥ 0
t ≤ 1
By applying the value of t, we get
√(1 - √(1 - x2)) ≤ 1
1 - √(1 - x2)) ≤ 1
Subtracting 1 through out the equation,
- √(1 - x2)) ≤ 0
√(1 - x2)) ≥0
Taking squares on both sides,
(1 - x2) ≥ 0
- x2 ≥ -1
x ≤ 1
Hence the domain is x ∈ [-1, 1]
Question 6 :
If f (x) = x2 , g(x) = 3x and h(x) = x −2 , Prove that (f ∘ g) ∘ h = f ∘ (g ∘ h) .
Solution :
L.H.S :
(f ∘ g) ∘ h
(f ∘ g) = f[g(x)]
(f ∘ g) = f[3x]
Now we have to apply 3x as x in the function f(x)
f(3x) = (3x)2
f(3x) = 9x2
(f ∘ g) ∘ h = (f ∘ g) [h(x)]
= (f ∘ g) [x - 2]
Now we have to apply x - 2 as x in the function (f ∘ g)
= 9(x - 2)2
= 9(x2 - 4x + 4)
= 9x2 - 36x + 36 ---------(1)
R.H.S :
f ∘ (g ∘ h)
(g ∘ h) = g[h(x)]
(g ∘ h) = g[x - 2]
Now we have to apply x - 2 as x in the function g(x)
g(x - 2) = 3(x - 2)
(g ∘ h) = 3x - 6
f ∘ (g ∘ h) = f [3x - 6]
Now we have to apply 3x - 6 as x in the function f(x)
= (3x - 6)2
= 9x2 - 36x + 36 ---------(2)
Hence proved.
Question 7 :
Let A = {1, 2} and B = {1, 2, 3, 4} , C = {5, 6} and D = {5, 6 ,7, 8} . Verify whether A × C is a subset of B × D?
Solution :
A = {1, 2} and C = {5, 6}
A x C = {(1, 5) (1, 6) (2, 5) (2, 6)} ----(1)
B = {1, 2, 3, 4} and D = {5, 6 ,7, 8}
B x D = { (1, 5) (1, 6) (1, 7) (1, 8) (2, 5) (2, 6) (2, 7) (2, 8) (3, 5) (3, 6) (3, 7) (3, 8) (4, 5) (4, 6) (4, 7) (4, 8) }
Hence A x C is the subset of B x D.
Question 8 :
If f(x) = (x - 1)/(x + 1), x ≠ 1 show that f(f(x)) = -1/x, provided x ≠ 0
Solution :
f(x) = (x - 1)/(x + 1) (Given)
f(f(x)) =
Hence proved.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Jul 27, 24 04:58 AM
Jul 27, 24 04:44 AM
Jul 27, 24 04:15 AM