# Find composition of $f{\left(x \right)} = 8 x^{2} - 10 x$ and $g{\left(x \right)} = 9 x - 7$

The calculator will find the composition of the functions $f{\left(x \right)} = 8 x^{2} - 10 x$ and $g{\left(x \right)} = 9 x - 7$, with steps shown.

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Find the composition of $f{\left(x \right)} = 8 x^{2} - 10 x$ and $g{\left(x \right)} = 9 x - 7$.

### Solution

$\left(f\circ g\right)\left(x\right) = f\left(g\left(x\right)\right) = f\left(9 x - 7\right) = 8 {\color{red}\left(9 x - 7\right)}^{2} - 10 {\color{red}\left(9 x - 7\right)} = 648 x^{2} - 1098 x + 462$

$\left(g\circ f\right)\left(x\right) = g\left(f\left(x\right)\right) = g\left(8 x^{2} - 10 x\right) = 9 {\color{red}\left(8 x^{2} - 10 x\right)} - 7 = 72 x^{2} - 90 x - 7$

$\left(f\circ f\right)\left(x\right) = f\left(f\left(x\right)\right) = f\left(8 x^{2} - 10 x\right) = 8 {\color{red}\left(8 x^{2} - 10 x\right)}^{2} - 10 {\color{red}\left(8 x^{2} - 10 x\right)} = 4 x \left(4 x - 5\right) \left(32 x^{2} - 40 x - 5\right)$

$\left(g\circ g\right)\left(x\right) = g\left(g\left(x\right)\right) = g\left(9 x - 7\right) = 9 {\color{red}\left(9 x - 7\right)} - 7 = 81 x - 70$

$\left(f\circ g\right)\left(x\right) = 648 x^{2} - 1098 x + 462$A
$\left(g\circ f\right)\left(x\right) = 72 x^{2} - 90 x - 7$A
$\left(f\circ f\right)\left(x\right) = 4 x \left(4 x - 5\right) \left(32 x^{2} - 40 x - 5\right)$A
$\left(g\circ g\right)\left(x\right) = 81 x - 70$A