How do you find #(g*h)(x)# given #f(x)=x^2-1 and #g(x)=2x-3# and #h(x)=1-4x#?

1 Answer
smendyka
Mar 12, 2017

See the entire solution process below:

Explanation:

#(g * h)(x) = g(x) * h(x) = (2x - 3) * (1 -4x)#

#(g * h)(x) = (color(red)(2x - 3))(color(blue)(1 -4x))#

#(g * h)(x) = (color(red)(2x) xx color(blue)(1)) - (color(red)(2x) xx color(blue)(4x)) - (color(red)(3) xx color(blue)(1)) + (color(red)(3) xx color(blue)(4x))#

#(g * h)(x) = 2x - 8x^2 - 3 + 12x#

#(g * h)(x) = -8x^2 + 2x + 12x - 3#

#(g * h)(x) = -8x^2 + (2 + 12)x - 3#

#(g * h)(x) = -8x^2 + 14x - 3#

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