If f(x)=4[x-1] and g(x)=x+1, how do you find f(g(-1))?

1 Answer
Aldrich
Sep 11, 2015

#f(g(-1)) = -4#

Explanation:

When you have an expression:
#f(y)# ,
this means that you should plug in whatever #y# is into #x# in the function #f(x)#. That is, replace every instance of #x# with #y#.

There are two ways to find #f(g(-1))#
The first is to solve from the inside out.

Plug in #-1# into #g(x)# to get #g(-1)#:
#g(x) = x+1#
#g(-1) = -1 +1#
#color(blue)(g(-1) = 0)#

Then, plug in #g(-1)# into #f(x)#:
#f(x) = 4[x-1]#
#f(g(-1)) = 4[0-1]#
#color(blue)(f(g(-1)) = -4)#

The second way is to get #f(g(x))# first, then plug in #-1#:

#color(red)(f(x) = 4[x-1])#
#color(blue)(g(x) = x+1)#

#color(red)(f(color(blue)(g(x)))) = color(red)(4[color(blue)(x+1)-1])#

Then, you can plug in #-1#

#f(g(-1)) = 4[-1 +1 -1]#
#color(blue)(f(g(-1)) = -4)#

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