Operations on Functions

Front

What is the definition of function subtraction?

Back

Function subtraction is the operation of subtracting one function from another, defined as (f-g)(x) = f(x) - g(x).

Front

If f(x) = 3x^2 - 4 and g(x) = x^2 - 8x + 4, what is (f-g)(x)?

Back

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

Front

What is the formula for function multiplication?

Back

Function multiplication is defined as (f*g)(x) = f(x) * g(x).

Front

If f(x) = 3x^2 - 2x + 1 and g(x) = x - 4, what is (f*g)(x)?

Back

(f*g)(x) = 3x^3 - 14x^2 + 9x - 4.

Front

What does f(g(x)) represent?

Back

f(g(x)) represents the composition of functions, where g(x) is substituted into f(x).

Front

If f(x) = x^2 + x and g(x) = 3x + 1, what is the value of f(g(4))?

Back

f(g(4)) = 182.

Front

What is the definition of function composition?

Back

Function composition is the operation of applying one function to the results of another, defined as (f∘g)(x) = f(g(x)).

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, what is g(h(x))?

Back

g(h(x)) = 9x + 1.

Front

What is the difference between a polynomial function and a linear function?

Back

A polynomial function can have multiple terms with varying degrees, while a linear function is a polynomial of degree one, represented as f(x) = mx + b.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.