Operations on Functions

Operations on Functions - How it Works - Video

Operation Chart

Operation Chart:

Here we have our four different operation chart: sum, difference, product, and quotient. We have to be careful with the parentheses when dealing with functions. Remember that function(input) = output.

f(x) = 1 function and g(x) is another function (although it can be the same as f(x).

(f + g) means that we have combined like terms of each function, f and g, already, so when we insert our input value (x), we only have to find one output value (y). You can substitute the input value (x) into each function, f and g, and then do an operation, but might involve more steps.

The same goes with (f - g), (f * g), and (f / g).

Example 1 - Sum

Example 1 - Sum:

The first operation that we are going to do is sum.

Right now we have two separate functions f(x) = 2x + 3 and g(x) = -4x + 5. Since we want to add, let's add the two functions together.

Now we know (f + g)(x) = -2x + 8 because (f + g)(x) = f(x) + g(x).

Our input value is 4. So let's substitute that into what we have.

So (f + g)(4) = 0 or the sum of the two functions when 4 is inserted is 0.

Let's check our work. Remember we can find the value of each function with the same input value (x) and do the operation that is required.

Here we found f(4) and g(4).

Now that we know f(4) and g(4), we can find the sum. f(4) + g(4) => (11) + (-11) => 0.

So we combined the functions and substituted one value and find our answer. We also found the individual vale of each function and found the sum that way as well. Both answers are the same that means we did it correctly. 

Example 1 - Difference

Example 1 - Difference:

The second operation that we are going to do is difference.

Right now we have two separate functions f(x) = 2x + 3 and g(x) = -4x + 5. Since we want to subtract, let's subtract the two functions.

Now we know (f - g)(x) = 6x - 2 because (f - g)(x) = f(x) - g(x).

Our input value is 4. So let's substitute that into what we have.

So (f - g)(4) = 22 or the difference of function f and function g when 4 is inserted is 0.

Let's check our work. Remember we can find the value of each function with the same input value (x) and do the operation that is required.

Here we found f(4) and g(4).

Now that we know f(4) and g(4), we can find the difference. f(4) + g(4) => (11) - (-11) => 22.

So we combined the functions and substituted one value and find our answer. We also found the individual vale of each function and found the difference that way as well. Both answers are the same that means we did it correctly. 

Example 1 - Product

Example 1 - Product:

The third operation that we are going to do is product.

Right now we have two separate functions f(x) = 2x + 3 and g(x) = -4x + 5. Since we want to multiply, let's multiply the two functions.

Now we know (f * g)(x) = -8x2  - 2x + 15 because (f * g)(x) = f(x) * g(x).

Our input value is 4. So let's substitute that into what we have.

So (f * g)(4) = -121 or the product of function f and function g when 4 is inserted is -121.

Let's check our work. Remember we can find the value of each function with the same input value (x) and do the operation that is required.

Here we found f(4) and g(4).

Now that we know f(4) and g(4), we can find the product. f(4) * g(4) => (11) * (-11) => -121.

So we combined the functions and substituted one value and find our answer. We also found the individual vale of each function and found the product that way as well. Both answers are the same that means we did it correctly. 

Example 1 - Quotient

Example 1 - Quotient:

The fourth operation that we are going to do is quotient.

Right now we have two separate functions f(x) = 2x + 3 and g(x) = -4x + 5. Since we want to divide, let's divide the two functions.

Now we know (f / g)(x) = (2x + 3) / (-4x + 5) because (f / g)(x) = f(x) / g(x).

Our input value is 4. So let's substitute that into what we have.

So (f / g)(4) = -1 or the quotient of function f and function g when 4 is inserted is -1.

Let's check our work. Remember we can find the value of each function with the same input value (x) and do the operation that is required.

Here we found f(4) and g(4).

Now that we know f(4) and g(4), we can find the sum. f(4) + g(4) => (11) / (-11) => -1.

So we combined the functions and substituted one value and find our answer. We also found the individual vale of each function and found the quotient that way as well. Both answers are the same that means we did it correctly. 

Live Worksheet

Teacher - Edpuzzle Link