Which is linear?

Hello Guest!

Which is linear

f(x) = (1/2)2x

or

f(x) = -1/2 (x-2) ?

f(x) = (1/2)2x

$f(x) = \frac{1}{2}\times 2x$

f(x) = x

f(x) is linear                      a straight {nl}  

f(x) = -1/2 (x-2)

$f(x)= \frac{-1}{2(x-2)}$

$f(x) = \frac{ 1}{ 4- 2x}$

f (x) is non-linear             a hyperbola {nl}  

Greeting asinus :- )

  !

I am not sure that the syntax is accurate. If the first equation should be

$f(x)=({1\over2})^{2x}$

then it is not linear. 

For x=0, f=1

For x=1, f=1/4

For x=2, f=1/16

If the second equation should be

$f(x)=-{1\over{2}}*(x-2)$

Then you can simplify to $f(x)=-{x\over{2}}+1$

which is linear. See that

For x=0, f=1

For x=1, f=1.5

For x=2, f=2

If asinus is correct then you can ignore this.

I am not sure that the syntax is accurate. If the first equation should be

$f(x)=({1\over2})^{2x}$

then it is not linear. 

For x=0, f=1

For x=1, f=1/4

For x=2, f=1/16

If the second equation should be

$f(x)=-{1\over{2}}*(x-2)$

Then you can simplify to $f(x)=-{x\over{2}}+1$

which is linear. See that

For x=0, f=1

For x=1, f=0.5

For x=2, f=0

EDIT: I forgot the minus there, whoops.