Adding Functions

Using Function Notation

Addition

You will be given two functions. First add them together. Then combine any like terms.

This is shown as: f(x)=5x+4 and g(x)=6x-2

then (f+g)(x)=5x+4+6x-2

(f+g)(x)=11x+2

Multiple Choice

Which of the following is the notation for adding two functions, f(x) and g(x) together?

• (f+g)(x)

• (fg)(x)

• (f-g)(x)

• ( $$\frac{f}{g}$$ )(x)

Multiple Choice

What is (f+g)(x) if f(x)=7x-3 and g(x)=2x+5?

• 9x-2

• 9x+2

• 5x+2

• 5x-2

Multiple Choice

Find $$\left(f+g\right)\left(x\right)$$ if $$f\left(x\right)=3x^2-2x+5$$ and $$g\left(x\right)=x^2+6x-7$$

• $$3x^2+4x+2$$

• $$4x^2+4x+2$$

• $$4x^2+4x-2$$

• $$4x^2+8x-2$$

Plugging in Numbers

Evaluate the function for a certain number

If the parenthesis after the (f+g) have something other than x in them then you will plug that number in as x after you're done adding.

Example

​If f(x)=2x²+3x-5 and g(x)=x²-x+6, the find (f+g)(2)

So first add f(x) and g(x) together

2x²+3x-5+x²-x+6=3x²+2x+1

Then plug in 2 as the x-value: 3(2)²+2(2)+1

=3(4)+4+1

=12+4+1

=17

Multiple Choice

If f(x)=5x+7 and g(x)=-2x-4, find (f+g)(2)

• 10

• 12

• 17

• 9

Multiple Choice

If $$f\left(x\right)=6x^2+3x-2$$ and $$g\left(x\right)=-2x^2-5x+9$$ then find (f+g)(1).

NOT TWO THIS TIME, PLUG IN ONE.

• 9

• 10

• 11

• 12