Basic Operations with Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

What does f(x) represent in a function?

Back

f(x) represents the output of the function f for a given input x.

Front

How do you 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

What is the formula for (f + g)(x) if f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1?

Back

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

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute that value into the function's equation.

Front

Evaluate f(x) = -2t^2 + 1 for f(-3).

Back

f(-3) = -17.

Front

What does it mean to find the value of x for f(x) = -2?

Back

It means to solve the equation f(x) = -2 for x.

Front

For what value of x does f(x) = -2 if f(x) = -2x + 2?

Back

x = -5.

Front

What is the formula for (f/g)(x)?

Back

To find (f/g)(x), divide the output of f(x) by the output of g(x): (f/g)(x) = f(x) / g(x).

Front

Given f(x) = x^2 + 5 and g(x) = 2x^3 - 1, find (f/g)(-3).

Back

(f/g)(-3) = -14/55.