ShmoopTube

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Thank you We sneak and here's your shmoop du jour

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Brought to you by fancy footwork Now that's a dancer

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with some fancy feet Yeah All right If f of

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x equals x squared minus four X minus three and

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g f x equals two x plus five What is

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f of g of x and hear the pencil answers

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All right Difference in size Something here Okay well in

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english this roughly translates to give this of that Is

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this and that of this is that what is this

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of that of that Make even less sense now doesn't

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want let's stick with the math version so we can

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solve this one with little substitution and just a bit

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of fancy footwork We're told that g f x equals

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two x plus five So when we're given this nasty

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looking thing at the end we can plug in two

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x plus five in place of g f x to

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get f of the quantity Two Acts plus 5 well

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from here we can plug in that same expression as

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acts throughout the function F of x so f of

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x equals x squared minus four X minus three and

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that becomes f of the quantity Two x plus five

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equals the quantity two x plus five squared minus four

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times the quantity Two x plus five minus three it's

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longer but simpler Go figure Now we can just multiply

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everything out to simplify to x plus five square and

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we'll have to use the distributive property to get four

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x squared plus ten x plus ten x plus twenty

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five The next part multiplies out negative eight x minus

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twenty and finally there's that negative three on the end

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reminding all like terms it looks like f of the

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quantity two x plus five equals four x squared plus

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twelve x plus two which is option d Well that

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certainly was easier than we thought it would be that

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what dance our way to the answer although i suppose

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we could have completed it even faster if we've done 00:01:56.441 --> [endTime] the hustle

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