Combine Functions

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

• -9x+11

• 4x²+4x

• 9x+1

• 9x+11

Find f(n) - g(n)

• x² - 2x + 6

• -x² + 2x + 4

• -x² - 2x - 6

• x² - 2x - 4

f(n)= n² + 4n
g(n)= - n - 5
Find f(n) + g(n)

• n² + 3n - 5

• -n³ + 2n - 7

• n³ + 3n - 3n

• n² - 3n - 5

f(x) = x³ - 3x
g(x) = -4x + 1
Find f(x)*g(x)

• -4x³ - 5x² - 3

• -4x³ + 2x² - 3x

• -4x⁴ + x³ +12x² - 3x

• -4x⁴ - x³ + 12x² + 3x

Determine (f + g)(x) for the following functions. f(x) = x^2, g(x) = sqrt{x}.

• x^2 + sqrt{x}

• x^2 - sqrt{x}

• x^2 * sqrt{x}

• x^2 / sqrt{x}

If the functions do not __________ , they cannot be combined.

• share a domain

• have the same range

• intersect at a point

• have the same codomain

Determine (f + g)(x), (f - g)(x), and (g - f)(x) for the following functions. f(x) = 4, g(x) = 2.5.

• (f + g)(x) = 6.5, (f - g)(x) = 1.5, (g - f)(x) = -1.5

• (f + g)(x) = 6.5, (f - g)(x) = 1.5, (g - f)(x) = 1.5

• (f + g)(x) = 6.5, (f - g)(x) = -1.5, (g - f)(x) = 1.5

• (f + g)(x) = 6.5, (f - g)(x) = -1.5, (g - f)(x) = -1.5

Combine the given equations using the appropriate operation, then simplify by collecting like terms. Example 1: Given the discrete functions below, find: f(x) = {(1, 4), (2, -3), (3, 0), (4, 2), (5, -1)} g(x) = {(1, 6), (3, 7), (5, -3), (7, 1), (9, -4)} a) (f + g)(x) Remember to consider the domain of each function!

• {(1, 10), (3, 7), (5, -4)}

• {(1, 10), (3, 7), (5, -1)}

• {(1, 10), (3, 7), (5, -4), (7, 1), (9, -4)}

• {(1, 10), (2, -3), (3, 7), (4, 2), (5, -4)}

Algebraically: Combine the given equations using the appropriate operation, then simplify by collecting like terms. Example 1: Given the discrete functions below, find: f(x) = {(1, 4), (2, -3), (3, 0), (4, 2), (5, -1)} g(x) = {(1, 6), (3, 7), (5, -3), (7, 1), (9, -4)} b) (f - g)(x) Remember to consider the domain of each function!

• {(1, -2), (3, -7), (5, 2)}

• {(1, -2), (3, -7), (5, 2), (7, 1), (9, -4)}

• {(1, 10), (3, 7), (5, 2)}

• {(1, 10), (3, 7), (5, 2), (7, 1), (9, -4)}

Combine the given equations using the appropriate operation, then simplify by collecting like terms. Example 1: Given the discrete functions below, find: f(x) = {(1, 4), (2, -3), (3, 0), (4, 2), (5, -1)} g(x) = {(1, 6), (3, 7), (5, -3), (7, 1), (9, -4)} c) (g - f)(x) Remember to consider the domain of each function!

• (1, 2), (3, 7), (5, -3)

• (1, 2), (3, 7), (5, -2)

• (1, 2), (3, 7), (5, -4)

• (1, 2), (3, 7), (5, -1)