Find the function composition $f \circ g (x) = f (g (x))$ $f@g(x)=f(g(x))$ where $f (x) = 8 x - 18$ $f(x ) = 8x-18$ and $g (x) = \frac{1}{2} x - 1$ $g(x) = 1/2x-1$ ?

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Find the function composition $f \circ g (x) = f (g (x))$ $f@g(x)=f(g(x))$ where $f (x) = 8 x - 18$ $f(x ) = 8x-18$ and $g (x) = \frac{1}{2} x - 1$ $g(x) = 1/2x-1$ ?

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Answer 1 · 2017-10-06T01:40:14

$f (g (x)) = 4 x - 26$ $f(g(x)) = 4x-26$
$g (f (x)) = 4 x - 10$ $g(f(x)) =4x-10$

Explanation:

We have:

$f (x) = 8 x - 18$ $f(x ) = 8x-18$
$g (x) = \frac{1}{2} x - 1$ $g(x) = 1/2x-1$

And so

$f (g (x)) = f (\frac{1}{2} x - 1)$ $f(g(x)) = f(1/2x-1)$
$= 8 (\frac{1}{2} x - 1) - 18$ $" " = 8(1/2x-1)-18$
$= 4 x - 8 - 18$ $" " = 4x-8-18$
$= 4 x - 26$ $" " = 4x-26$

And:

$g (f (x)) = g (8 x - 18)$ $g(f(x)) =g(8x-18)$
$= \frac{1}{2} (8 x - 18) - 1$ $" " = 1/2(8x-18)-1$
$= 4 x - 9 - 1$ $" " = 4x-9-1$
$= 4 x - 10$ $" " = 4x-10$

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Find the function composition $f \circ g (x) = f (g (x))$ $f@g(x)=f(g(x))$ where $f (x) = 8 x - 18$ $f(x ) = 8x-18$ and $g (x) = \frac{1}{2} x - 1$ $g(x) = 1/2x-1$ ?