Answer:
The function f(x) when x=x-4 is [tex]f(x-4)=3x^2-24x+53[/tex] or [tex]f(x-4)=3x(x-8)+53[/tex]
Step-by-step explanation:
Given function f is defined by [tex]f(x)=3x^2+5[/tex]
Now to find the function f(x-4):
[tex]f(x)=3x^2+5[/tex]
Put x=x-4 in the above function we get
[tex]f(x-4)=3(x-4)^2+5[/tex]
[tex]f(x-4)=3(x^2-2(x)(4)+4^2)+5[/tex] (using the formula [tex](a-b)^2=a^2-2ab+b^2[/tex])
[tex]f(x-4)=3(x^2-8x+16)+5[/tex]
[tex]f(x-4)=3x^2-24x+48+5[/tex] (adding the like terms)
[tex]f(x-4)=3x^2-24x+53[/tex]
[tex]f(x-4)=3x(x-8)+53[/tex]
Therefore [tex]f(x-4)=3x^2-24x+53[/tex] or [tex]f(x-4)=3x(x-8)+53[/tex]
The function f(x) when x=x-4 is [tex]f(x-4)=3x^2-24x+53[/tex] or [tex]f(x-4)=3x(x-8)+53[/tex]
