# Functions f and g are defined by f(x)=3/x and g(x)=2x+1.Express x=(x-1)/2 in terms of f or/and g

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You need to express the equation `x=(x-1)/2` in terms of `f(x) = 3/x` and `g(x) = 2x + 1` such that:

`x=(x-1)/2`

You need to multiply by 2 both sides such that:

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

Reducing duplicate factors yields:

`2x = x - 1 `

You need to add 1 both sides, such that:

`2x + 1 = x`

Notice that the equation `2x + 1` is the equation of the function `g(x) = 2x + 1` , hence, you may substitute `g(x)` for `2x + 1` such that:

`g(x) = x`

You need to divide by 3 both sides, such that:

`g(x)/3 = x/3`

Notice that the function `f(x) = 3/x` , hence `x/3` `= 1/(f(x)), ` thus, you may substitute `1/(f(x))` for `x/3` such that:

`g(x)/3 = 1/(f(x))`

You need to perform cross mutliplication such that:

`3*1 = f(x)g(x)`

**Hence, using the equation of the functions `f(x)` and `g(x)` yields that you may write the expression `x=(x-1)/2` in terms of `f(x)` and `g(x)` such that `f(x)g(x) = 3` .**

x=(x-1)/2

2x=x-1

2x+1=x

g(x)=3/f(x)

f(x)g(x)=3

Given f(x)=3/x and g(x)= 2x + 1

he given equation => x = (x-1)/2

Or, 2x = x -1

Or, 2x + 1 = x

Or, g(x) = 3/(fx) [ since, g(x)=2x+1, x= 3/)f(x) ]

Or, g(x)*f(x)=3

**Hence, g(x)*f(x) = 3 <--- Answer**

Given : f(x) = 3/x and g(x) = 2x + 1

f(x) = 3/x

Or, x = 3/f(x) -------- (1) And g(x)= 2x + 1 -----(2)

Given equation :

x = (x - 1)/2

Or, 2x = x - 1

Or, 2x + 1 = x

Or, g(x) = 3/f(x) [ substituting value of 2x+1 from eq.(1) and value of x from eq.(2) ]

Or, g(x).f(x) = 3

Or, f(x).g(x) = 3

**Hence x = (x - 1)/2 is equivalent to : **

** f(x).g(x)= 3 Answer**