Question

Write a rule for g(x)=-f(2x) when f(x)= 1/2x³ x²-4x-5?

Answer 1

To write the rule for g(x) = -f(2x) when f(x) = 1/(2x³ x²-4x-5), substitute the expression for f(x) into the rule for g(x) and simplify.

Step-by-step explanation:

To write a rule for g(x) = -f(2x) when f(x) = 1/(2x³ x²-4x-5), we need to substitute the expression for f(x) into the rule for g(x). Let's break it down step by step:

1. Start with the rule for g(x): g(x) = -f(2x)
2. Substitute the expression for f(x): g(x) = -[1/(2(2x)³ (2x)²-4(2x)-5)]
3. Simplify the expression inside the brackets: g(x) = -[1/(16x³ 4x²-8x-5)]
4. Simplify the negative sign: g(x) = 1/(16x³ 4x²-8x-5)

So the rule for g(x) in terms of f(x) is g(x) = 1/(16x³ 4x²-8x-5).