f(x) = x+4
g(x) =
x-1
To find a function such that g * f =
h.
Solution:
The
operation
We interpret that The function h(x) is to be
determined and not g which is already known (or given).
We
interpret the operation (or composition) * as (i)multiplication (ii) any operation
or composition.
(i) * is mutiplying
operation.
If a*b = ab , or a multiplied by b, then h(x) =
g*f = (x+4)(x-1) = x^2+3x-4. So h(x) = x^2+3x-4.
(ii) * is
any operation or composition of two functions:
If the
composition is a*b = a^2-b^2 , then h(x) = [g(x)]^2 - {f(x)]^2 = (x+4)^2-(x-1)^2 =
x^2+8x+16 - (x^2-2x+1) = 10x+15.
If the composition is a*b
= a - b , then h(x) = g(x) - f(x) = x+4 -(x-1) = 5.
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