How do you find $g(f(2))$ given $g(n)=3n+2$ and $f(n)=2n^2+5$ ?

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Answer 1 · 2017-05-07T19:57:27

See a solution process below:

First, find $f(2)$ by substituting every occurrence of $color(red)(n)$ with $color(red)(2)$ in the function $f(n)$ and calculate the result:

$f(color(red)(n)) = 2color(red)(n)^2 + 5$ becomes:

$f(color(red)(2)) = (2 * color(red)(2)^2) + 5$

$f(color(red)(2)) = (2 * 4) + 5$

$f(color(red)(2)) = 8 + 5$

$f(color(red)(2)) = 13$

Now, we know $g(f(2)) = g(13)$

To find $g(13)$ substitute every occurrence of $color(red)(n)$ with $color(red)(13)$ in the function $g(n)$ and calculate the result:

$g(color(red)(n)) = 3color(red)(n) + 2$ becomes:

$g(color(red)(13)) = (3 * color(red)(13)) + 2$

$g(color(red)(13)) = 39 + 2$

$g(color(red)(13)) = 41$

$g(f(2)) = 41$

How do you find g(f(2))g(f(2)) given g(n)=3n+2g(n)=3n+2 and f(n)=2n^2+5f(n)=2n^2+5?