Question #a0d1e

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Answer 1 · 2017-03-19T16:02:00

#f(5) = 7#

#f(5) = f(2+3)# which means #x = 2#

#f(2+5) = 2(2)^2 - 3(2) + 5 = 8 - 6 + 5 = 7#

Answer 2 · 2017-03-19T16:16:38

There are at least two ways to do this problem; please see the explanation for both.

#f(5)=7#

Let #g(x) = x + 3#, then:

#g(g^-1(x))= g^-1(x)+3#

#x = g^-1(x)+3#

#g^-1(x)=x-3#

Therefore, we can obtain #f(x)# by substituting #x-3# for #x# into #f(x+3)#

#f(x-3+3)=2(x-3)^2-3(x-3)+5#

#f(x) = 2(x^2-6x+9) - 3x+9+5#

#f(x) = 2x^2-12x+18-3x+14#

#f(x) = 2x^2-15x+32#

Evaluate at #x = 5#:

#f(5) = 2(5)^2-15(5)+32#

#f(5) = 7#

Alternatively we could have evaluated #f(x+3)# at #x = 2#:

#f(2+3)= 2(2)^2 -3(2)+5#

#f(5)= 7#