function q (1 Viewer)

[anonymoushehe]

heyy can someone pls explain the solution, like I'm not getting it

 

[WeiWeiMan]

heyy can someone pls explain the solution, like I'm not getting it

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Flawed question but it's basically making 2x-3 equal to some 2(something) + something

 

[cossine]

heyy can someone pls explain the solution, like I'm not getting it

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Basically the key idea is to introduce new variable. We can define the variable t however we want. In this case it is best to define it as t=1-x

From this definition we can rewrite the equation:

f(1-x) = 2x-3 as

f(t) = 2(1-t) -3 # This is through substitution

simplification leads to f(t) = -2t -1

Note that we now have the answer we desire we have just replace x with t.

This leads to the answer f(x) = -2x-1

 

[cossine]

Flawed question but it's basically making 2x-3 equal to some 2(something) + something

The question is not flawed.

 

[anonymoushehe]

So the first step would be to figure out what you don't get. Basically they find f(t). f(t) is f(x) just you have replace x with t.

I’m confused about lettting t equal 1 - x, do you mind explaining?

Flawed question but it's basically making 2x-3 equal to some 2(something) + something

ohhhhh ty!

 

[anonymoushehe]

Basically the key idea is to introduce new variable. We can define the variable t however we want. In this case it is best to define it as t=1-x

From this definition we can rewrite the equation:

f(1-x) = 2x-3 as

f(t) = 2(1-t) -3 # This is through substitution

simplification leads to f(t) = -2t -1

Note that we now have the answer we desire we have just replace x with t.

This leads to the answer f(x) = -2x-1

Wait I understand it but up until when u said that u replace x with t. Wasnt t originally 1 - x so it would be f(1-x) = -2x - 1 instead?

 

[cossine]

Wait I understand it but up until when u said that u replace x with t. Wasnt t originally 1 - x so it would be f(1-x) = -2x - 1 instead?

So we have f(t) = -2t-1. We know that t=1-x. so if you undo the substitution you will get f(1-x) = -2(1-x) -1 = -2x -3. But this is not we want.

We know that f(t) =-2t-1. We replace t with x on BOTH sides.

To give another example

Suppose we have f(t) = -2t -1.

This will mean f(z) = -2z-1 or similarly f(y) = -2y-1. We replacing in this t with the inputs of the function in this case z and y respectively.

 

[anonymoushehe]

So we have f(t) = -2t-1. We know that t=1-x. so if you undo the substitution you will get f(1-x) = -2(1-x) -1 = -2x -3. But this is not we want.

We know that f(t) =-2t-1. We replace t with x on BOTH sides.

To give another example

Suppose we have f(t) = -2t -1.

This will mean f(z) = -2z-1 or similarly f(y) = -2y-1. We replacing in this t with the inputs of the function in this case z and y respectively.

Wait sorry for being dumb why do we not want that specific form?? Appreciate the help btw!!

 

[cossine]

Wait sorry for being dumb why do we not want that specific form?? Appreciate the help btw!!

specific form??

So the question is asking for f(x). So although you could give f(t) instead it is not exactly what question asks for.

 

[anonymoushehe]

specific form??

So the question is asking for f(x). So although you could give f(t) instead it is not exactly what question asks for.

OHHHHHHH that makes sense omg thank you so muchhhhh I can finally sleep now