Find the function

[candid hare]

Can someone help I haven't solved something similar before

Only the i)

[abstract timber]

can you translate it?

[candid hare]

Yes

It says to find f(x)

From the equation

[wind glade]

sub x=1-x

$$2f(x)-f(1-x)=x^2+2x-1$$
$$2f(1-x)-f(x)=(1-x)^2+2(1-x)-1=x^2-4x+2$$
$$f(x)+f(1-x)=2x^2-2x+1$$

[toxic grove]

Schlaumau

[wind glade]

Add the first and the last equation to get $3f(x)=3x^2$

[toxic grove]

Schlaumau

[wind glade]

$f(x)=x^2$

[toxic grove]

Schlaumau

[wind glade]

@candid hare

[candid hare]

How did you converted to 3x²

[candid hare]

How did you made the 3rd part

[wind glade]

To get the third equation I added the first two

[candid hare]

Ok

Thanks @wind glade