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# Worked example: evaluating expressions with function notation

Evaluating -2⋅f(-6)+g(1) given the graphs of f and g. Created by Sal Khan.

Video transcript

We're asked to evaluate
negative 2 times f of negative 6 plus g of 1. 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 6 is. So our input into our
function is negative 6. And we'll assume that's
along the horizontal axis. So our input is negative 6. And based on our function
definition, f of negative 6 is 7. So this thing. Let me write this down. f
of negative 6 is equal to 7. And what is g of 1? Well, once again,
here's our input axis. And then the function
says that g of 1, which is right over
there, is negative 5. g of 1 is equal to negative 5. So this statement simplifies
to negative 2 times f of negative 6, which is 7. So times 7 plus g of
1, which is negative 5. So plus negative 5, which
simplifies to-- let's see. Negative 2 times 7 is
negative 14 plus negative 5, which is negative 19. And we are done.