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If $f (x) = 3 x$ $f(x)=3x$ and $g (x) = 4 x - 3$ $g(x)=4x-3$ , how do you find f[g(5)] and g[f(5)]?

1 Answer

Jul 23, 2015

Evaluate $a = g (5)$ $a = g(5)$ then substitute the value of $a$ $a$ for the argument $g (5)$ $g(5)$ in $f (g (5))$ $f(g(5))$ and evaluate $f (a)$ $f(a)$ for this argument.
(Similarly for $g (f (5))$ $g(f(5))$ )

Explanation:

$f (x) = 3 x$ $f(x)=3x$ $XXXXXX$ $color(white)("XXXXXX")$ $\to$ $rarr$ $XXXX$ $color(white)("XXXX")$ $f (5) = 15$ $f(5) = 15$

$g (x) = 4 x - 3$ $g(x) = 4x-3$ $XXXX$ $color(white)("XXXX")$ $\to$ $rarr$ $XXXX$ $color(white)("XXXX")$ $g (5) = 17$ $g(5) = 17$

$f (g (5)) = f (17)$ $f(g(5)) = f(17)$
$XXXX$ $color(white)("XXXX")$ $= 3 (17) = 51$ $= 3(17) = 51$

$g (f (5) = g (15)$ $g(f(5) = g(15)$
$XXXX$ $color(white)("XXXX")$ $= 4 (15) - 3 = 57$ $= 4(15) -3 = 57$

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