college algebra

[girlpower]

If f(x) =2x+1 and g(x)= x-1/2, then f(g (x).

So I got x f (2x+1)=x

2x+1 /2 =x-1/2

then x+1 =x-1 and sutract 1 and got 0 is this correct help me

 

[DrPhil]

If f(x) =2x+1 and g(x)= x-1/2, then f(g (x).

So I got x f (2x+1) = x

2x+1 /2 =x-1/2

then x+1 =x-1 and sutract 1 and got 0 is this correct help me

Not correct, but I appreciate that you showed your work.

When we say
f(x) = 2x + 1
the "x" is just a name for any number, and f(x) is twice that number plus 1
For instance, we could just as well use the name "g" in place of "x":
f(g) = 2g + 1

But the name "g" can also be replaced by g(x) = x - 1/2. We just substitute the expression in place of the name.
f(g(x)) = 2(x - 1/2) + 1 = . . .

 

[HallsofIvy]

If f(x) =2x+1 and g(x)= x-1/2, then f(g (x).

So I got x f (2x+1)=x

Why is that "x" in front of f? In any case, f(x)= 2x+ 1. It does NOT follow that "f(2x+1)= x".

2x+1 /2 =x-1/2

then x+1 =x-1 and sutract 1 and got 0 is this correct help me

\(\displaystyle f(g(x))= f(x- 1/2)= 2(x- 1/2)+ 1. Reduce that.\)