Use the function to evaluate the indicated expressions and simplify

Question

f(x)= 3x^2 +4

f(x+2) =

f(x) + f(2) =

Answer 1

Julianne, it’s actually not so hard.

f(x+2) = 3(x+2)² + 4

because you need to replace “x” with “x+2”

now multiply that our and simplify.

similarly,

f(x) + f(2) = 3x² + 4 + 3(2)² + 4

now multiply those out , add and simplify.

Answer 2

Given: f(x) = 3x² +4

To find f(x+2), wherever you see x in the orginal given equation, you substitute (x+2) as such:

f(x+2) = 3(x+2)² + 4, which equals: 3(x² + 2x + 2x + 4) + 4 = 3(x² + 4x + 4) + 4 = 3x² + 12x +12 + 4,

finally adding the constants, the final answer:

3x² + 12x + 16

Part 2:

f(x) = 3x² + 4 (given)

then, for f(2), replace x with 2, which gives us:

f(2) = 3(2)² + 4 = 3(4) + 4 finally, f(2) = 12 + 4 = 16

adding the two functions per the question [ f(x) + f(2) ] gives us

3x² + 4 + 16 = 3x² +20

Hope this helps,

kind regards