If $f (x) = x^{2} + 4 x$ $f(x)=x^2+4x$ and $g (x) = 3 x - 5$ $g(x)=3x-5$ , how do you find $(f (g (x))$ $(f(g(x))$ and $g (f (x))$ $g(f(x))$ ?

Question

If $f (x) = x^{2} + 4 x$ $f(x)=x^2+4x$ and $g (x) = 3 x - 5$ $g(x)=3x-5$ , how do you find $(f (g (x))$ $(f(g(x))$ and $g (f (x))$ $g(f(x))$ ?

1 Answer

Impact of this question

6577 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-02-19T13:39:55

It might be better if we think of the functions as having different parameters, so

If $f (a) = a^{2} + 4 a$ $f(a)=a^2+4a$
and $g (b) = 3 b - 5$ $g(b)=3b−5$ ,

then
$f (g (x))$ $f(g(x))$ simply means re-writing the $f (a)$ $f(a)$ equation with $a$ $a$ replaced by $g (x)$ $g(x)$ :
$f (g (x))$ $f(g(x))$
$= ({g (x)}^{2} + 4 (g (x))$ $= (g(x)^2 + 4(g(x))$
$= {(3 x - 5)}^{2} + 4 (3 x - 5)$ $= (3x - 5)^2 + 4(3x -5)$
$= 9 x^{2} - 18 x + 5$ $= 9x^2 -18x +5$

Similarly
$g (f x))$ $g(fx))$
$= 3 (x^{2} + 4 x) - 5$ $= 3(x^2 + 4x) - 5$ (by replacing $b$ $b$ with $f (x)$ $f(x)$ )
$= 3 x^{2} + 12 x$ $= 3x^2 + 12x$

Science

Math

Humanities

... and beyond

If $f (x) = x^{2} + 4 x$ $f(x)=x^2+4x$ and $g (x) = 3 x - 5$ $g(x)=3x-5$ , how do you find $(f (g (x))$ $(f(g(x))$ and $g (f (x))$ $g(f(x))$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

If f(x)=x2+4xf(x)=x^2+4x and g(x)=3x−5g(x)=3x-5, how do you find (f(g(x))(f(g(x)) and g(f(x))g(f(x))?

1 Answer

Related questions

Impact of this question

If $f (x) = x^{2} + 4 x$ $f(x)=x^2+4x$ and $g (x) = 3 x - 5$ $g(x)=3x-5$ , how do you find $(f (g (x))$ $(f(g(x))$ and $g (f (x))$ $g(f(x))$ ?