Given $f (x) = \frac{3 x - 1}{2 x + 5}$ $f(x) = (3x-1 )/( 2x+5)$ and $g (x) = \frac{7 x + 3}{3 x - 1}$ $g(x)=( 7x+3 )/( 3x-1)$ how do you find f(g(x))?

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Answer 1 · 2016-05-06T17:19:23

$f (g (x)) = \frac{18 x + 10}{11 x + 7}$ $f(g(x))=(18x+10)/(11x+7)$

$f (x) = \frac{3 x - 1}{2 x + 5}$ $f(x)=(3x-1)/(2x+5)$ and $g (x) = \frac{7 x + 3}{3 x - 1}$ $g(x)=(7x+3)/(3x-1)$

we get $f (g (x))$ $f(g(x))$ by putting $g (x)$ $g(x)$ in place of $x$ $x$ in $f (x)$ $f(x)$ .

Hence $f (g (x)) = \frac{3 \cdot \frac{7 x + 3}{3 x - 1} - 1}{2 \cdot \frac{7 x + 3}{3 x - 1} + 5}$ $f(g(x))=(3*(7x+3)/(3x-1)-1)/(2*(7x+3)/(3x-1)+5)$

= $\frac{3 (7 x + 3) - (3 x - 1)}{2 (7 x + 3) - (3 x - 1)}$ $(3(7x+3)-(3x-1))/(2(7x+3)-(3x-1))$

= $\frac{21 x + 9 - 3 x + 1}{14 x + 6 - 3 x + 1}$ $(21x+9-3x+1)/(14x+6-3x+1)$

= $\frac{18 x + 10}{11 x + 7}$ $(18x+10)/(11x+7)$

Given f(x)=3x−12x+5f(x) = (3x-1 )/( 2x+5) and g(x)=7x+33x−1g(x)=( 7x+3 )/( 3x-1) how do you find f(g(x))?