Given f(x) = 3x +1 and (f o g)(x) = 6 - 1/2x, how do you find the function g?

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Given f(x) = 3x +1 and (f o g)(x) = 6 - 1/2x, how do you find the function g?

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Answer 1 · 2016-06-27T13:42:56

$g (x) = \frac{5}{3} - \frac{1}{6} x$ $g(x)=5/3-1/6x$

Explanation:

$f (x) = 3 x + 1$ $f(x)=3x+1$
$(f \circ g) (x) = 6 - \frac{1}{2} x$ $(f@g)(x)=6-1/2x$
'~~~~~~~~~~~~~~~~~~~~~~~~~
$\Rightarrow 3 [g (x)] + 1 = 6 - \frac{1}{2} x$ $=>3[g(x)]+1=6-1/2x$

$3 [g (x)] = 5 - \frac{1}{2} x \leftarrow subtract 1 from both sides$ $3[g(x)]=5-1/2x" "larr" subtract 1 from both sides"$

$g (x) = \frac{5}{3} - \frac{1}{6} x \leftarrow divide both sides by 3$ $g(x)=5/3-1/6x" "larr" divide both sides by 3"$

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Given f(x) = 3x +1 and (f o g)(x) = 6 - 1/2x, how do you find the function g?

1 Answer

Explanation:

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