Let f(x)=8x-1, and g(x)=x/2 how do you find (fg(x))?

1 Answer
George C.
Aug 10, 2015

Write #f(u) = 8u-1#, then substitute #u = g(x)# to get:

#f(g(x)) = f(u) = 8u - 1 = 8g(x) - 1 = 8(x/2)-1#

#= 4x-1#

Explanation:

It's slightly easier to see if you use a different variable name for the definition of #f#, for example #f(u) = 8u-1#. Note that the variable name does not really matter - it is just a place-holder for a value.

Then substitute #u = g(x)# to get:

#f(g(x)) = f(u) = 8u - 1 = 8g(x) - 1 = 8(x/2)-1#

#= 4x-1#

Alternatively, describe #f(g(x))# as a sequence of steps, then construct a formula from those steps to simplify:

(1) Divide by #2#
(2) Multiply by #8#
(3) Subtract #1#

So #f(g(x)) = (x/2)*8 - 1 = 4x-1#

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