FINDING COMPOSITION FUNCTION WITH THREE FUNCTIONS

Given f(x) = -2x + 1, g(x) = x2, and h(x) = -1/2x + 1/2, evaluate the following:

Problem 1 :

Given f(x) = -2x + 1, find f(-6)

Solution:

f(x) = -2x + 1

f(-6) = -2(-6) + 1

= 12 + 1

f(-6) = 13

Problem 2 :

Given g(x) = x2, find g(-3)

Solution:

g(x) = x2

g(3) = -32

= 9

Problem 3 :

Given h(x) = -1/2x + 1/2, find h(4)

Solution:

h(x)=-12x+12h(4)=-12(4)+12=-2+12=-32

Problem 4 :

Given f(x) = -2x + 1, g(x) = x2, find f [g(2)]

Solution:

f [g(x)] = f[x2]

= -2(x2) + 1

f [g(x)] = -2x2 + 1

f [g(2)] = -2(2)2 + 1

= -8 + 1

= -7

Problem 5 :

Given h(x) = -1/2x + 1/2, g(x) = x2, find h [g(8)]

Solution:

h [g(x)] = h[x2]

h[g(x)]=-12x2+12h[g(8)]=-1282+12=-12(64)+12=-642+12=-632

Problem 6 :

Given f(x) = -2x + 1, g(x) = x2, find (g ∘ f) (5)

Solution:

(g ∘ f) (x) = g [f(x)]

= g[-2x + 1]

g [f(x)] = (-2x + 1)2

g [f(5)] = (-2(5) + 1)2

= (-10 + 1)2

= (-9)2

= 81

Problem 7 :

Given g(x) = x2, and h(x) = -1/2x + 1/2, (g ∘ h) (7)

Solution:

(g ∘ h) (x) = g [h(x)]

=g -12x+12g[h(x)]=-12x+122g[h(7)]=-12(7)+122=-72+122=(-3)2=9

Problem 8 :

Given f(x) = -2x + 1, g(x) = x2, and h(x) = -1/2x + 1/2, find f [g(c)]

Solution:

f [g(x)] = f[x2]

= -2(x2) + 1

f [g(x)] = -2x2 + 1

f [g(c)] = -2(c)2 + 1

= -2c2 + 1

Problem 9 :

Given f(x) = -2x + 1, g(x) = x2, and h(x) = -1/2x + 1/2, find f [h(5)]

Solution:

f[h(x)]=f-12x+12=-2-12x+12+1f[h(5)]=-2-12(5)+12+1=-2-52+12+1=-2(-2)+1=4+1=5

Problem 10 :

Given f(x) = -2x + 1 and h(x) = -1/2x + 1/2, h [f(r)]

Solution:

h[f(x)]=h[-2x+1]=-12(-2x+1)+12h[f(r)]=-12(-2r+1)+12

Problem 11 :

Given f(x) = -2x + 1, g(x) = x2, and h(x) = -1/2x + 1/2, find h[g[f(3)]]

Solution:

g[f(x)] = g[-2x + 1]

= (-2x + 1)2

g[f(3)] = (-2(3) +1)²

= (-6 + 1)2

= -5²

= 25

h[g[f(3)]] = h[25]

=-12(25)+12=-252+12=-242=-12

Problem 12 :

Given f(x) = -2x + 1, g(x) = x2, and h(x) = -1/2x + 1/2, find (f ∘ g ∘ h)(3)

Solution:

(f ∘ g ∘ h)(x) = f[g[h(x)]]

g[h(x)]=g-12x+12=-12x+122g[h(3)]=-12(3)+122=-32+122=(-1)2g[h(3)]=1f[g[h(3)]]=f(1)=-2(1)+1=-2+1=-1

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