Answer:
Step-by-step explanation:
1) Composite functions are function of two or more functions to serve as one function. For example, given d(x) and g(x), we can write both as composite function as d(g(x)). We can call it function of a function. Hence, from the following function, the following options except option B are composite.
d(x)g(x) is the product of the two functions not a composite.
Option B is correct.
b) Given h(x) = x-1 and d(x) = 7x+3
H(3) = 3-1
H(3) = 2
d(2) = 7(2)+3
d(2) = 14+3
d(2) = 17
h(3)+d(2) = 2+17
h(3)+d(2) = 19 (option D)
c) Given t(x) = -x² + 7x + 1 and r(x) = 5x² - 2x + 8, we are to first find the function
t(x)-r(x)
t(x)-r(x) = -x²+7x+1-5x²+2x-8
t(x)-r(x) = -x²-5x²+7x+2x+1-8
t(x)-r(x) = -6x²+9x-7
Substitute x as 2
(t-r)(2) = -6(2)²+9(2)-7
t-r (2) = -6(4)+18-7
(t-r)(2) = -24+11
(t-r)(2) = -13 (option C)
d) If h(x) = 4x + 2 and g(x) = 3x - 1,
h-g = 4x+2-(3x-1)
h-g = 4x+2-3x+1
h-g = 4x-3x+2+1
h-g = x+3
h-g(4) = 4+3
(h-g)(4) = 7
e) If g(x) = x - 4 and h(x) = x + 5, we are to find f(x)h(x)
h(x)g(x) = (x-4)(x+5)
h(x)g(x) = x(x)+5x-4x-20
h(x)g(x) = x²+x-20
Hence the product of h(x) and g(x) is x²+x-20. Option D is correct
