Question

If f(x) = -0.5x + 2.5 what is f(x) = 0 and what is f(0) ?

Answer 1

1.
`x=5, f(x)=0`,
`f(5)=0`

2.
`x=0, f(x)=2.5`,
`f(0)=2.5`

Explanation:

We have the expression:
`f(x)=-0.5x+2.5`

First we are going to calculate
`f(x)=0` this is:

`f(x)=0\\-0.5x+2.5=0`

We can subtract 2.5 from both sides of the equation,

`-0.5x+2.5=0\\-0.5x+2.5-2.5=-2.5\\-0.5x=-2.5`

Now, divide both sides in (-0.5),

`-0.5x=-2.5\\\\(-0.5x)/(-0.5)=(-2.5)/(-0.5)\\\\x=5`

This means that for

`x=5, f(x)=0`

or you can rewrite it as:

`f(5)=0`

Now we have to calculate
`f(0)`, this means that we have to replace
`f(x)` with
`x=0`. This is:

`f(x)=-0.5x+2.5\\f(0)=-0.5(0)+2.5\\f(0)=0+2.5\\f(0)=2.5`

`x=0, f(x)=2.5`

or rewrite it as

`f(0)=2.5`

Answer 2

a) To find x for f(x) = 0, substitute the given information and solve for x.
.. f(x) = 0 = -0.5x +2.5
.. 0.5x = 2.5 . . . . . . . . . . add 0.5x
.. x = 2.5/0.5 = 5 . . . . . . divide by the coefficient of x

f(5) = -0.5*5 +2.5 = 0


b) f(0) = -0.5*0 +2.5 = 2.5