Let the function f be defined by f(x)=2x-1 if 1/2f(square root of t)=4 what is the value of t. please explain?

Question

what does it mean when a number is in front of f(x) what do they want me to, for example like the 1/2

Answer 1

It's actually simple algebra. It's used as an example involving residue theory. This is in relation to residue theory.

example:

f ( x ) = 3 / ( x + 1 )  + 3 / ( x + 1 ) ^ 2

...now factor 3 / ( x + 1 ) from both terms...

f ( x ) = 3 / ( x  + 1 )  x  ( 1 + 1 / ( x + 1 ) )

...now if I multiply ( x + 1 ) to both side of the equation, the solution looks a little funny

( x + 1 ) f ( x ) = 3 ( 1 + 1 / ( x + 1 ) )

or

( x + 1 ) f ( x ) = 3  + 3 / ( x + 1 ) )

I'll provide a link which explains.

Answer 2

the 1/2 in front of the f(x) means that you should take the result of f(x) and multiply it by 1/2

1/2(f(sqrt(t)))=4 divide by 1/2

f(sqrt(t))=8

8=2x-1

9=2x

x=9/2

sqrt(t)=9/2

therefore,

t=81/4