Answer: 18x+24
Step-by-step explanation:
[tex]f(x+3)=3(x+3)^2 + 5\\\\f(x+3)=3(x^2 + 6x+9)+5\\\\f(x+3)=3x^2+18x+27+5\\\\f(x+3)=3x^2 + 18x+32[/tex]
[tex]\therefore f(x+3)-[f(x)+3]=(3x^2 +18x+32)-[3x^2 +5+3]\\ \\=3x^2 +18x+32-3x^2 - 8\\\\=\boxed{18x+24}[/tex]
If function f(x) = 3x² + 5 then the value of f(x + 3) - [f(x) + 3] is 18x + 24.
Given the function f(x) = 3x² + 5.
We have to find the value of f(x + 3) - [f(x) + 3]
First we have to find the value of f(x + 3) - [f(x) + 3]
f(x + 3) = 3 (x + 3) ² + 5f(x + 3)
= 3(x ² + 6x + 9) + 5f(x + 3)
= 3x ² + 18x + 27 + 5f(x + 3)
= 3x ² + 18x + 32
Now substitute these values and find the value of f(x + 3) - [f(x) + 3].
f(x + 3) - [f(x) + 3] = (3x² + 18x + 32) - [3x ^ 2 + 5 + 3]
=3x ² + 18x + 32 - 3x ² - 8
=18x + 24
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