How do you find #(gof)(x)# given #f(x)=x-1# and #g(x)=x^2+2x-8#?

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Answer 1 · 2017-08-02T23:15:41

Another notation is given by the following equation:

#(gof)(x) = g(f(x))#

We substitute #g(x) = x^2 + 2x -8 # on the right side but we write #(f(x))# everywhere that there is an x:

#(gof)(x) = (f(x))^2 + 2(f(x)) -8#

Substitute #x-1# for #f(x)#:

#(gof)(x) = (x-1)^2 + 2(x-1) -8#

Expand the square:

#(gof)(x) = x^2-2x + 1 + 2(x-1) -8#

Use the distributive property:

#(gof)(x) = x^2-2x + 1 + 2x-2 -8#

Combine like terms:

#(gof)(x) = x^2 -9 larr# answer