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

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Answer 1 · 2017-05-25T17:46:38

See a solution process below:

First, we can write #(g * h)(x)# as:

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

Next, we can substitute #color(red)(4)# for each occurrence of #color(red)(x)# in #(g * h)(x)# to find #(g * h)(4)#:

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

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

#(g * h)(color(red)(4)) = (8 - 3) * (1 - 16)#

#(g * h)(color(red)(4)) = 5 * -15#

#(g * h)(color(red)(4)) = -75#