Function Operations

Front

What is the definition of function operations?

Back

Function operations involve combining two or more functions using addition, subtraction, multiplication, or division to create a new function.

Front

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

Back

(f + g)(x) = f(x) + g(x)

Front

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

Back

(f - g)(x) = f(x) - g(x)

Front

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

Back

(f * g)(x) = f(x) * g(x)

Front

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

Back

(f / g)(x) = f(x) / g(x), where g(x) ≠ 0.

Front

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

Back

(f + g)(x) = 2x + 1 + x^2 = x^2 + 2x + 1.

Front

Given f(x) = 3x - 4 and g(x) = 5x + 2, find (f - g)(x).

Back

(f - g)(x) = (3x - 4) - (5x + 2) = -2x - 6.

Front

Given f(x) = x + 1 and g(x) = 2x, find (f * g)(x).

Back

(f * g)(x) = (x + 1)(2x) = 2x^2 + 2x.

Front

Given f(x) = x^2 - 1 and g(x) = x - 1, find (f / g)(x).

Back

(f / g)(x) = (x^2 - 1) / (x - 1) = x + 1, for x ≠ 1.

Front

What is the value of f(0) if f(x) = -3x + 3?

Back

f(0) = -3(0) + 3 = 3.