Find composition of f(x)=8x210xf{\left(x \right)} = 8 x^{2} - 10 x and g(x)=9x7g{\left(x \right)} = 9 x - 7

The calculator will find the composition of the functions f(x)=8x210xf{\left(x \right)} = 8 x^{2} - 10 x and g(x)=9x7g{\left(x \right)} = 9 x - 7, with steps shown.

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Find the composition of f(x)=8x210xf{\left(x \right)} = 8 x^{2} - 10 x and g(x)=9x7g{\left(x \right)} = 9 x - 7.

Solution

(fg)(x)=f(g(x))=f(9x7)=8(9x7)210(9x7)=648x21098x+462\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

(gf)(x)=g(f(x))=g(8x210x)=9(8x210x)7=72x290x7\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

(ff)(x)=f(f(x))=f(8x210x)=8(8x210x)210(8x210x)=4x(4x5)(32x240x5)\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)

(gg)(x)=g(g(x))=g(9x7)=9(9x7)7=81x70\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

Answer

(fg)(x)=648x21098x+462\left(f\circ g\right)\left(x\right) = 648 x^{2} - 1098 x + 462A

(gf)(x)=72x290x7\left(g\circ f\right)\left(x\right) = 72 x^{2} - 90 x - 7A

(ff)(x)=4x(4x5)(32x240x5)\left(f\circ f\right)\left(x\right) = 4 x \left(4 x - 5\right) \left(32 x^{2} - 40 x - 5\right)A

(gg)(x)=81x70\left(g\circ g\right)\left(x\right) = 81 x - 70A