Addition and Subtraction of Functions

Front

Define the addition of functions.

Back

The addition of functions is the operation where two functions, f(x) and g(x), are combined to form a new function (f + g)(x) = f(x) + g(x).

Front

What is the formula for subtracting two functions?

Back

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

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^2 + 2x + 3.

Front

Calculate (f - g)(x) if f(x) = 3x^2 and g(x) = x + 1.

Back

(f - g)(x) = 3x^2 - (x + 1) = 3x^2 - x - 1.

Front

What is the result of f(n) - g(n) if f(n) = n^2 + 1 and g(n) = 2n - 5?

Back

f(n) - g(n) = (n^2 + 1) - (2n - 5) = n^2 - 2n + 6.

Front

Find (f + g)(2) if f(x) = x^2 and g(x) = 3x.

Back

(f + g)(2) = (2^2) + (3*2) = 4 + 6 = 10.

Front

What is the value of (f - g)(x) if f(x) = 5x^2 + 3x and g(x) = 8x?

Back

(f - g)(x) = (5x^2 + 3x) - (8x) = 5x^2 - 5x.

Front

If g(x) = x^2 - 36x and m(x) = x + 2, what is (m - g)(x)?

Back

(m - g)(x) = (x + 2) - (x^2 - 36x) = -x^2 + 37x + 2.

Front

What does (f + g)(x) represent in function operations?

Back

(f + g)(x) represents the combined output of functions f and g for any input x.

Front

If f(x) = 9 - 3x and g(x) = 5x - 7, find (f + g)(x).

Back

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