Question #21600

If f = (1, 2), (2, 3), (3, 4), (4, 5),
g = (1, -2), (3, -3), (5, -5), and
h = (1, 0), (2, 1), (3, 2),
find the following and state the domain:
g * f * h

Expert's answer

Determine value of x where all function (f, h) are defined:

x = 1 -> f(1) = 2, g(1) = -2 and h(1) = 0

x = 3 -> f(3) = 4, g(3) = -3 and h(3) = 2

Find function f*h*g when x = 1, 3:

f*h*g(1) = f(1)*g(1)*h(1) = 2*(-2)*0 = 0

f*h*g(3) = f(3)*g(3)*h(3) = 4*(-3)*2 = -24

So f*g*h& = (1, 0), (3, -24)

domain of a function is the set of "input" or argument values (x) for which the function is defined, so

domain: {1, 3}

x = 1 -> f(1) = 2, g(1) = -2 and h(1) = 0

x = 3 -> f(3) = 4, g(3) = -3 and h(3) = 2

Find function f*h*g when x = 1, 3:

f*h*g(1) = f(1)*g(1)*h(1) = 2*(-2)*0 = 0

f*h*g(3) = f(3)*g(3)*h(3) = 4*(-3)*2 = -24

So f*g*h& = (1, 0), (3, -24)

domain of a function is the set of "input" or argument values (x) for which the function is defined, so

domain: {1, 3}

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