Worked example: evaluating expressions with function notation

we're asked to evaluate negative two times F of the negative six plus G of one and they've defined at least graphically f of X and G of X here below so let's see how we can evaluate this well to do this we first have to figure out what f of negative six is so our input into our function is negative six so and we'll assume that's along the horizontal axis so our input is negative six and based on our function definition F of negative six F of negative six is seven so this thing let me write this down F of negative six is equal to seven and what is G of one G G of one well once again here's our input axis and then the function says the G of one which is right over there is negative five G of one is equal to negative five so this statement simplifies to negative two times F of negative six which is seven so times seven plus plus G of one which is negative 5 so plus negative five which simplifies to let's see negative two times 7 is negative 14 plus negative 5 which is negative 19 and we are done