If f(x)=(1/x), find in simplest form: 3 f(x-1) + 2?

Question

Step by step PLEASE...

Answer 1

3f(x -1) + 2
= 3/(x -1) +2
= [3 + 2(x -1) ]/(x -1)
= (2x +1)/(x -1)

Answer 2

f(x) = 1/x
x is just a stand-in, it could just as well be, say, u:
f(u) = 1/u
or
f(elephant) = 1/elephant
(You may not be confused about that, but some people are)

Anyway, if you let u = x-1 (which you can because, again, u is just a stand-in and could be anything), you get:
f(u) = 1/u ──► f(x-1) = 1 / (x-1)

So
3*f(x-1) + 2 = [3 / (x-1)] + 2

You can make this a simple fraction by multiplying the 2 by (x-1)/(x-1):

3/(x-1) + 2(x-1)/(x-1) = 3/(x-1) + (2x-2)/(x-1)
= (3 + 2x - 2) / (x - 1) = (2x+1) / (x-1)

Answer 3

if by this you mean

3f(x - 1) + 2, then

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

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

Answer 4

Given f(x) = (1/x)
or f(y) = (1/y) where y=x-1
Therefore,
f(x-1) = (1/(x-1))
Now 3f(x-1) + 2 = 3* (1/(x-1)) +2
= 3/(x-1) +2
= ( 3 + 2(x-1))/(x-1) ( By taking LCM)
= ( 3 + 2x -2)/ (x-1)
= ( 2x + 1)/(x-1).


Hope I did what you wanted!

Answer 5

3 f(x-1) + 2
= 3 /(x-1) +2
= [3+2(x-1) ]/(x-1)
= (2x-1)/(x-1)

Answer 6

f(x)=(1/x)
3*1/(x-1)+2
3+2x-2/(x-1)
=2x-1/(x-1)