Final answer:
To evaluate f(x-4) for f(x)=2x²-3x+5, replace x with (x-4) in the original function and simplify to get 2x² - 19x + 49.
Step-by-step explanation:
When asked to evaluate f(x-4) given the function f(x)=2x²-3x+5, you will substitute (x-4) into the function wherever there is an x. This operation gives:
f(x-4) = 2(x-4)² - 3(x-4) + 5
Now, you need to expand the square and simplify the expression:
f(x-4) = 2(x² - 8x + 16) - 3x + 12 + 5
Simplify further by distributing the 2 and combining like terms:
f(x-4) = 2x² - 16x + 32 - 3x + 12 + 5
f(x-4) = 2x² - 19x + 49
Therefore, the evaluated function f(x-4) is 2x² - 19x + 49.