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. It is denoted as (f o g)(x) = f(g(x)).

Front

If f(x) = x - 4, what is f(2)?

Back

f(2) = 2 - 4 = -2.

Front

If g(x) = 8x - 2, what is g(1)?

Back

g(1) = 8(1) - 2 = 6.

Front

If h(x) = -4x + 3, what is h(-1)?

Back

h(-1) = -4(-1) + 3 = 4 + 3 = 7.

Front

Calculate g(h(-1)) if g(x) = 8x - 2 and h(x) = -4x + 3.

Back

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

Front

Calculate f(h(2)) if f(x) = x - 4 and h(x) = -4x + 3.

Back

f(h(2)) = f(-5) = -5 - 4 = -9.

Front

What is the notation for function composition?

Back

The notation for function composition is (f o g)(x), which means f(g(x)).

Front

If h(x) = x + 5 and k(x) = 5x + 1, what is h o k(5)?

Back

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

Front

Calculate g(f(2)) if f(x) = x - 4 and g(x) = 8x - 2.

Back

g(f(2)) = g(-2) = 8(-2) - 2 = -16 - 2 = -18.

Front

Calculate h(g(2)) if h(x) = -4x + 3 and g(x) = 8x - 2.

Back

h(g(2)) = h(14) = -4(14) + 3 = -56 + 3 = -53.