Composition of Functions Weekly HW

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function, denoted as (f o g)(x) = f(g(x)).

Front

If f(x) = 3x + 6, what is f(2)?

Back

f(2) = 3(2) + 6 = 12.

Front

What does g(f(2)) represent?

Back

g(f(2)) means to first find f(2) and then apply the function g to that result.

Front

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

Back

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

Front

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

Back

f o g(-3) = f(g(-3)) = f(-3) = 3(-3) + 6 = -9 + 6 = -3.

Front

If h(x) = x + 5, what is h(5)?

Back

h(5) = 5 + 5 = 10.

Front

What is the value of g(h(-1)) if g(x) = 8x - 2 and h(x) = x + 5?

Back

g(h(-1)) = g(4) = 8(4) - 2 = 32 - 2 = 30.

Front

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

Back

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

Front

If h(g(2)) = 3, what does this imply about the functions h and g?

Back

It implies that the output of g(2) is such that when it is input into h, the result is 3.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.