Problem 1 :
Let f(x) = 2x2 - 3 and g(x) = 4x.
Evaluate the following :
(i) f ∘ g(1)
(ii) g ∘ f(1)
(iii) (f ∘ f)(-2)
(iv) (g ∘ g)(-1)
Problem 2 :
Let f(x) = 2x - 1, g(x) = 3x and h(x) = x2 + 1.
Evaluate the following :
(i) f ∘ g(-3)
(ii) f ∘ h(7)
(iii) (g ∘ h)(24)
(iv) f{g[h(2)]}
Problem 3 :
Let f(x) = x, g(x) = 12x and h(x) = 6/x.
Evaluate the following :
(i) f ∘ g(5)
(ii) f ∘ h(-1)
(iii) (h ∘ f)(3)
Problem 4 :
Let f(x) = -4x + 2 and g(x) = √(x - 8).
Evaluate : f ∘ g(12).
Problem 5 :
Let f(x) = -2x + 1 and g(x) = √(x2 - 5).
Evaluate : g ∘ f(2).
Problem 6 :
Let f(x) = log10x and g(x) = 10x.
Evaluate : f ∘ g(5).
1. Solution :
f(x) = 2x2 - 3 and g(x) = 4x
(i) f ∘ g(1) :
f ∘ g(1) = f[g(1)]
= f[4(1)]
= f(4)
= 2(4)2 - 3
= 2(16) - 3
= 32 - 3
= 29
(ii) g ∘ f(1) :
g ∘ f(1) = g[2(1)2 - 3]
= g[2(1) - 3]
= g(2 - 3)
= g(-1)
= 4(-1)
= -4
(iii) f ∘ f(-2) :
f ∘ f(-2) = f[2(-2)2 - 3]
= f[2(4) - 3]
= f(8 - 3)
= f(5)
= 2(5)2 - 3
= 2(25) - 3
= 50 - 3
= 47
(iii) g ∘ g(-1) :
g ∘ g(-1) = g[4(-1)]
= g(-4)
= 4(-4)
= -16
2. Solution :
f(x) = 2x - 1, g(x) = 3x and h(x) = x2 + 1
(i) f ∘ g(-3) :
f ∘ g(-3) = f[g(-3)]
= f[3(-3)]
= f(-9)
= 2(-9) - 1
= -18 - 1
= -19
(ii) f ∘ h(7) :
f ∘ h(7) = f[h(7)]
= f(72 + 1)
= f(49 + 1)
= f(50)
= 2(50) - 1
= 100 - 1
= 99
(iii) g ∘ h(24) :
g ∘ h(24) = g[h(24)]
= g(242 + 1)
= g(576 + 1)
= g(577)
= 3(577)
= 1731
(iv) f{g[h(2)]} :
f{g[h(2)]} = f{g[22 + 1]}
= f{g[4 + 1]}
= f{g(5)}
= f{3(5)}
= f(15)
= 2(15) - 1
= 30 - 1
= 29
3. Solution :
f(x) = x, g(x) = 12x and h(x) = 6/x
(i) f ∘ g(5) :
f ∘ g(5) = f[g(5)]
= f[12(5)]
= f(60)
= 60
(ii) f ∘ h(-1) :
f ∘ h(-1) = f[h(-1)]
= f[6/(-1)]
= f(-6)
= -6
(iii) h ∘ f(3) :
h ∘ f(3) = h[f(3)]
= h(3)
= 6/3
= 2
4. Solution :
f(x) = -4x + 2 and g(x) = √(x - 8)
f ∘ g(12) = f[g(12)]
= f[√(12 - 8)]
= f(√4)
= f(2)
= -4(2) + 2
= -8 + 2
= -6
5. Solution :
f(x) = -2x + 1 and g(x) = √(x2 - 5)
g ∘ f(2) = g[f(2)]
= g[-2(2) + 1]
= g(-4 + 1)
= g(-3)
= √[(-3)2 - 5]
= √(9 - 5)
= √4
= 2
6. Solution :
f(x) = log10x and g(x) = 10x
f ∘ g(5) = f[g(5)]
= f(105)
= log10(105)
= 5log10(10)
= 5(1)
= 5
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
May 07, 24 09:17 AM
May 05, 24 12:25 AM
May 03, 24 08:50 PM