Operations of Functions

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.

Front

What does it mean to add two functions, f(x) and g(x)?

Back

To add two functions, you combine their outputs: (f + g)(x) = f(x) + g(x).

Front

How do you subtract one function from another?

Back

To subtract two functions, you find the difference of their outputs: (f - g)(x) = f(x) - g(x).

Front

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

Back

To multiply two functions, you multiply their outputs: (f * g)(x) = f(x) * g(x).

Front

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

Back

To divide two functions, you divide their outputs: (f / g)(x) = f(x) / g(x), where g(x) ≠ 0.

Front

If f(x) = x^2 and g(x) = x + 1, what is (f + g)(x)?

Back

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

Front

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

Back

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

Front

What is the domain of the function g(x) = 1/(x - 3)?

Back

The domain is all real numbers except x = 3, where the function is undefined.

Front

If f(x) = 3x^2 + 2 and g(x) = x, what is (f * g)(x)?

Back

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

Front

What is the result of (f / g)(x) if f(x) = x^2 + 1 and g(x) = x?

Back

(f / g)(x) = (x^2 + 1) / x, where x ≠ 0.