2.3-Composition Of Functions

Front

Define composition of functions.

Back

The composition of functions is a process where the output of one function becomes the input of another function. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the formula for finding f(g(x)) if f(x) = 2x + 3 and g(x) = x^2?

Back

f(g(x)) = f(x^2) = 2(x^2) + 3 = 2x^2 + 3.

Front

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

Back

f(2) = -2(2) + 3 = -4 + 3 = -1.

Front

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

Back

g(-3) = -3(-3) + 2 = 9 + 2 = 11.

Front

What is the result of g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

If f(x) = x^2 - 2 and g(x) = x + 9, find g(-2).

Back

g(-2) = -2 + 9 = 7.

Front

What is the value of h[f(g(-2))] if h(x) = -3x?

Back

h[f(g(-2))] = h[f(7)] = h[7^2 - 2] = h[49 - 2] = h[47] = -3(47) = -141.

Front

Define the term 'function'.

Back

A function is a relation that assigns exactly one output for each input from a set of inputs, known as the domain.

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) means applying g first and then f, while g(f(x)) means applying f first and then g. They are generally not equal.

Front

If f(x) = 2x + 1 and g(x) = x - 4, find f(g(5)).

Back

g(5) = 5 - 4 = 1; f(g(5)) = f(1) = 2(1) + 1 = 3.