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Core 3 Maths Questions

Hi Can someone please help me with the following questions;

1. Show that (a x e^-a) x (1-e^-a) can be written as e^a = 4a + 1

2. If f(x)=(x+1)/(x-1) and g(x)=1/x
Show f(x) = 1 + 2g(x-1)

Thank you!!

(edited 10 years ago)

Reply 1

shawn_o1

1. The first is an identity and the second is an expression, not sure what you're trying to ask.

2. consider g(x-1)

Reply 2

KSmith15

1. I have been told the area of a rectangle which is ae^-a, is 1/4 x (1-e^-a),so I have to show e^a=4a+1

Reply 3

KSmith15

Original post by shawn_o1

1. The first is an identity and the second is an expression, not sure what you're trying to ask.

2. consider g(x-1)

g(x-1) means f(x) should equal 1 +2/(x-1) but it actually equals (x+1)/(x-1)????

Reply 4

Liamnut

Your first question doesn't make sense. Post the whole thing.

For the second one,
g(x)=1/x so g(x-1)=1/(1-x)

Reply 5

TenOfThem

Original post by KSmith15

1. I have been told the area of a rectangle which is ae^-a, is 1/4 x (1-e^-a),so I have to show e^a=4a+1

This question still makes no sense

If you want help then post the question

Reply 6

TenOfThem

Original post by KSmith15

g(x-1) means f(x) should equal 1 +2/(x-1) but it actually equals (x+1)/(x-1)????

Can you add fractions

If so then add the

1

and the

\dfrac{2}{x-1}

Reply 7

KSmith15

Original post by TenOfThem

This question still makes no sense

If you want help then post the question

It is question 6

Original post by KSmith15

It is question 6

So, it is Q 7 and you completely omitted the 1/4 element of the question

What do you think the question tells you?

Reply 9

KSmith15

Original post by TenOfThem

So, it is Q 7 and you completely omitted the 1/4 element of the question

What do you think the question tells you?

I'm unsure 😔

Reply 10

TenOfThem

Original post by KSmith15

I'm unsure 😔

It tells you that 4 x (the area of the rectangle shown) = the area you found in part (i)

Reply 11

KSmith15

I tried to do that but I still couldn't get the equation they are asking for. I ended up with an equation with e^-a and they want e^a

Reply 12

TenOfThem

Original post by KSmith15

I tried to do that but I still couldn't get the equation they are asking for. I ended up with an equation with e^-a and they want e^a

then multiply through your equation by e^a

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