Function Operations and compositions

Front

Define function composition.

Back

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition of f and g is denoted as f(g(x)).

Front

What is the formula for adding two functions f(x) and g(x)?

Back

The formula for adding two functions is (f + g)(x) = f(x) + g(x).

Front

What is the formula for subtracting two functions f(x) and g(x)?

Back

The formula for subtracting two functions is (f - g)(x) = f(x) - g(x).

Front

What is the formula for multiplying two functions f(x) and g(x)?

Back

The formula for multiplying two functions is (f * g)(x) = f(x) * g(x).

Front

What is the formula for dividing two functions f(x) and g(x)?

Back

The formula for dividing two functions is (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

Given f(x) = 2x + 3 and g(x) = x^2, find f(g(2)).

Back

f(g(2)) = f(2^2) = f(4) = 2(4) + 3 = 11.

Front

If f(x) = x^2 and g(x) = 3x + 1, find g(f(3)).

Back

g(f(3)) = g(3^2) = g(9) = 3(9) + 1 = 28.

Front

What is the value of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

f(g(5)) = f(5 - 2) = f(3) = 3(3) + 10 = 19.

Front

If p(x) = 3x + 4 and q(x) = 2x^2, find q(p(-2)).

Back

q(p(-2)) = q(3(-2) + 4) = q(-2) = 2(-2)^2 = 8.

Front

What is the result of f(x) + g(x) if f(x) = 9 - 3x and g(x) = 5x - 7?

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.