Composition of functions

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RBlax

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Use composition of functions to determine whether f and g are inverses of one another.

Problem: f(x)=-1/2 x-1/2; g(x)=-2x+1

Here's what I've done:
f[g(x) ]=- 1/2 (-2x+1) - 1/2 = x-1
g[f(x) ]= -2 (- 1/2 x - 1/2) +1 = x+2

I don't know how to answer it tho. They are not exact inverses of one another, but on a graph they would show inverse.
 
Use composition of functions to determine whether f and g are inverses of one another.

Problem: f(x)=-1/2 x-1/2; g(x)=-2x+1

Here's what I've done:
f[g(x) ]=- 1/2 (-2x+1) - 1/2 = x-1
g[f(x) ]= -2 (- 1/2 x - 1/2) +1 = x+2

I don't know how to answer it tho. They are not exact inverses of one another, but on a graph they would show inverse.
Click to expand...

In order for two functions to be inverses of each other, the following must be true:

f[g(x) ] = g[f(x) ] = x

Your functions do not meet this criterion.
 
RBlax said:
Use composition of functions to determine whether f and g are inverses of one another.

Problem: f(x)=-1/2 x-1/2; g(x)=-2x+1

Here's what I've done:
f[g(x) ]=- 1/2 (-2x+1) - 1/2 = x-1
g[f(x) ]= -2 (- 1/2 x - 1/2) +1 = x+2

I don't know how to answer it tho. They are not exact inverses of one another, but on a graph they would show inverse.
Click to expand...

How did you decide that "on a graph they would show inverse".

These are vertically shifted from others inverses. It is hard to judge graphically.
 
Trust me it's been over 10 years since I touched this stuff. So the littlest help would be appreciated.

I already know that I'm challenged ;).
 
@ Subotosh

You're right, I honestly am lost in this topic so that's why I'm here =)
 
So the answer to your question is:

f(x) and g(x) are not inverse of each other because:

\(\displaystyle f[g(x)] \ \ = \ \ x-1 \ne x\)

and

\(\displaystyle g[f(x)] \ \ = \ \ x+2 \ne x\)
 
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