Let #f(x)=5x-1# and #g(x)=x^2-1#, what is #(f*g)(-1)#?

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Answer 1 · 2018-05-22T23:14:40

#-1#

First, we must find #f(g(x))# and then input #x=-1# into the function.

NOTE: #f(g(x))=(f*g)(x)#

I just prefer to write the composite function in the first way because I can conceptualize it better.

Getting back to the problem, to find #f(g(x))#, we start with our outside function, #f(x)#, and input #g(x)# into it.

#color(blue)(f(x)=5x-1)#, so wherever we see an #x#, we input #color(red)(g(x)=x^2-1)#. Doing this, we get

#color(blue)(5(color(red)(x^2-1))-1#

Let's distribute the #5# to both terms to get

#5x^2-5-1#

Which can obviously be simplified to

#f(g(x))=5x^2-6#

Recall that we want to know #f(g(-1))#, and we know #f(g(x))# now, so now we can plug in #-1# for #x#. Doing this, we get

#5(-1)^2-6#

#=5(1)-6#

#=5-6#

#f(g(-1))=-1#

Hope this helps!