Question

Create your own function to teach the Martians about functions. Your function must contain at least two different operations.
Using complete sentences, prove to Splott and Fizzle that your function is a legitimate function.
Using your function, explain to the Martians how to solve for f(3). Show your work and explain each step using complete sentences.
Using complete sentences, describe to the Martians how to find the inverse of your function.

Answer 1

The Martians ask you to explain one last thing, Ultimate Math Ambassador. They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2.

Answer 2

@KingGeorge Hey can you please come help us with this one thanks

Answer 3

Well the first bit is easy enough. Create a function. What's your favorite function?

Answer 4

thank you George

Answer 5

2x+6=4x+2

Answer 6

i just dont get how im supposed to plug f(3) into it then "The Martians ask you to explain one last thing, Ultimate Math Ambassador. They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2." @KingGeorge

Answer 7

So first of all, what you just gave me as a function, isn't really a function. It's an equation with the solution \(x=4\). So as a function, let's use \(f(x)=4x+2\). To plug in 3, all you have to do, is replace the \(x\) with \(3\).

So \(f(3)=f(3)+2=12+2=14\).

Answer 8

They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2
LOST lol

Answer 9

So now we create a new function \(h(x)\). For the sake of argument, let's suppose this function is \(2x+6\). Using this new function, can you tell me what \(h(3)\) is?

Answer 10

h(3)=6+6=12

Answer 11

Perfect. So \(f(h(3))=f(12)\). Plugging \(12\) into \(f(x)\), we get\[f(12)=4(12)+2=48+2=50.\]Repeating the same process, can you tell me what \(h(f(3))\) is? (recall that \(f(3)=14\))

Answer 12

i dont get this part. i just know h(14)= .. i dunno how to set it up

Answer 13

Well just by plugging in 14 to \(h(x)\), we get\[h(14)=2(14)+6=28+6=34.\]Now when we compare \(f(h(3))\) and \(h(f(3))\), we notice that \(f(h(3))=50\) and \(h(f(3))=34\). These numbers are not equal. So this means that \(f(h(x))\) and \(h(f(x))\) are NOT always the same number.

Answer 14

Thank you. Math gives me so much trouble.

Answer 15

You're welcome. Just remember that with enough practice, even math becomes easy.