Given $f (x) = x + 2$ $f(x)=x+2$ and $g (x) = x - 2$ $g(x)=x-2$ how do you find f(g(x))?

Question

Given $f (x) = x + 2$ $f(x)=x+2$ and $g (x) = x - 2$ $g(x)=x-2$ how do you find f(g(x))?

1 Answer

Impact of this question

1241 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-03T03:05:12

$f (g (x)) = x$ $f(g(x)) = x$

Explanation:

$f (g (x))$ $f(g(x))$ is denoting the composition of $f$ $f$ and $g$ $g$ . Just as how if we were applying $f$ $f$ to a number, we would substitute that number for each $x$ $x$ in $f (x)$ $f(x)$ , as we are applying to $f$ $f$ to $g (x)$ $g(x)$ , we substitute $g (x)$ $g(x)$ for each $x$ $x$ in $f (x)$ $f(x)$ .

$f (g (x)) = g (x) + 2 = (x - 2) + 2 = x$ $f(g(x)) = g(x)+2 = (x-2)+2 = x$

As a side note, because $f (g (x)) = g (f (x)) = x$ $f(g(x)) = g(f(x)) = x$ , we say that $f$ $f$ and $g$ $g$ are inverses of one another.

Science

Math

Humanities

... and beyond

Given $f (x) = x + 2$ $f(x)=x+2$ and $g (x) = x - 2$ $g(x)=x-2$ how do you find f(g(x))?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Given f(x)=x+2f(x)=x+2f(x)=x+2 and g(x)=x-2g(x)=x−2g(x)=x-2 how do you find f(g(x))?

1 Answer

Explanation:

Related questions

Impact of this question

Given $f (x) = x + 2$ $f(x)=x+2$ and $g (x) = x - 2$ $g(x)=x-2$ how do you find f(g(x))?