How do you find #f(g(4))# if #f(x)=2sqrt(x+3)# and #g(x)=-3x+1#?

1 Answer
mason m
Dec 24, 2015

#f(g(4))=4isqrt2#

Explanation:

First, find #g(4)#. Then, plug that value into #f(x)#.

Find #g(4)#:

#color(white)(xxxxxxx)g(4)=-3(4)+1#
#color(white)(xxxxxxx)g(4)=-11#

Find #f(g(4))#, which is equivalent to #f(-11)#:

#color(white)(xxxxxxx)f(-11)=2sqrt(-11+3)#
#color(white)(xxxxxxx)f(-11)=2sqrt(-8)#
#color(white)(xxxxxxx)f(-11)=2*2isqrt(2)#
#color(white)(xxxxxxx)f(-11)=4isqrt2#

Thus,

#color(white)(xxxxxxx)f(g(4))=4isqrt2#

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