Composition of Functions Weekly HW

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f o g)(x), is the process of applying one function to the results of another function. It is defined as (f o g)(x) = f(g(x)).

Front

If f(x) = 3x + 6, what is f(-1)?

Back

f(-1) = 3(-1) + 6 = 3.

Front

If g(x) = 2x + 3, what is g(0)?

Back

g(0) = 2(0) + 3 = 3.

Front

What is the value of f(g(-3)) if f(x) = 3x + 6 and g(x) = 2x + 3?

Back

f(g(-3)) = f(2(-3) + 3) = f(-3) = 3(-3) + 6 = -3.

Front

What is h(f(-2)) if h(x) = x + 5 and f(x) = 3x + 6?

Back

h(f(-2)) = h(3(-2) + 6) = h(0) = 0 + 5 = 5.

Front

If f(x) = x - 4, g(x) = 8x - 2, and h(x) = -4x + 3, what is g(h(-1))?

Back

g(h(-1)) = g(-4(-1) + 3) = g(7) = 8(7) - 2 = 54.

Front

What is the value of h(o)k(5) if h(x) = x + 5 and k(x) = 5x + 1?

Back

h(k(5)) = h(5(5) + 1) = h(26) = 26 + 5 = 31.

Front

What is f(f(-1)) if f(x) = 3x + 6?

Back

f(f(-1)) = f(3(-1) + 6) = f(3) = 3(3) + 6 = 15.

Front

What is the domain of the composition of functions?

Back

The domain of (f o g)(x) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.