If #f( x ) = 3x ^ { 2} - 4x + 4# , what is # f ( x - 1)#?

1 Answer
Rhys
Dec 2, 2017

#f(x-1) = 3x^2-10x+11#

Explanation:

if #f(x) = 3x^2-4x+4# then #f(delta) = 3delta^2-4delta+4#
and #f(x+alpha) = 3(x+alpha)^2-4(x+alpha)+4#
so where we see an #x# we replace with #x-1#;
#f(x-1) = 3(x-1)^2-4(x-1)+4#
#=3(x^2-2x+1)-4x+4+4#
#=3x^2-6x+3-4x+8#
#=3x^2-10x+11 = f(x-1)#

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