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:

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]

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)]

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:

Problem 10 :

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

Solution:

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]

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)]]