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Current time:0:00Total duration:4:10

CCSS.Math:

so we're told that G of X is equal to x squared plus 5x minus 3 and H of Y is equal to 3 times y minus 1 squared minus 5 and then we're asked what is H of G of negative 6 and this the way it's written might look a little strange to you this this little circle that we have in between the H and the G that's our function composition symbol so function function composition composition composition symbol and one way to rewrite this that might make a little bit more sense so this H of G of negative 6 you can rewrite this as this is going to be the same thing as G of negative 6 and then H of that so H of G of negative 6 notice I spoke this out the same way that I've said this this is H of G of negative 6 this is H of G of negative 6 I find the second notation far more intuitive but it's good to become familiar with this function composition notation this little circle because you might see that sometime and you shouldn't stress it's just the same thing as we have right over here now what is H of G of negative 6 and we just have to remind ourselves that this means that we're going to take the number negative 6 we're going to input it into our function G and then that will output G of negative 6 whatever that number is we'll figure it out in a second and then we're going to input that into our function H we're going to input that into our function H and then what we output is going to be H of G of negative 6 which is what we want to figure out G H of G of negative 6 so we just have to do it one step at a time a lot of times when you first start looking at these function composition it seems really convoluted and confusing but you just have to want you to take a breath and take it one step at a time well let's figure out what G of negative six is it's going to evaluate to a number in this case and then we input that number into the function H and then we'll figure out another that going to map to another number so G of negative 6 let's figure that out G of negative 6 is equal to negative 6 the squared plus 5 times negative 6 minus 3 which is equal to positive 36 minus 30 minus 3 so that's equal to what 36 minus 33 which is equal to 3 so G of negative 6 is equal to 3 G of negative 6 is equal to 3 G of negative 6 is equal to 3 you input negative 6 into G it outputs 3 and so H of G of negative 6 has now simplified to just H of 3 because G of negative 6 is 3 so let's figure out what H of 3 is H of 3 notice whatever we output it from G we're inputting that now into H so that's the number 3 so H of 3 is going to be 3 times 3 minus 1 3 minus 1 squared minus 5 which is equal to 3 times 2 squared this is 2 right over here minus 5 which is equal to 3 times 4 minus 5 which is equal to 12 minus 5 which is equal to 7 and we're done so you input negative 6 into G you get 3 and then you take that output from G and you put it into H and you get 7 so this right over here is 7 all of this has come out to be equal to 7 so H of G of negative 6 is equal to 7 H of G of negative 6 is equal to 7 input negative 6 into G take that output and input it into H and you're going to get 7