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Chapter 1: Problem 4

If \(f(x)=1 /\left(x^{3}+1\right),\) what is \(f(2) ?\) What is \(f\left(y^{2}\right) ?\)

Short Answer

Expert verified
Answer: f(2) = 1/9, and f(y虏) = 1/(y^6+1).

Step by step solution

01

Finding f(2)

First, we'll find the value of the function f(x) when x=2. We have: $$f(x) = \frac{1}{x^3+1}$$ Now, substitute x=2 into the function: $$f(2) = \frac{1}{(2)^3+1}$$
02

Simplifying f(2)

Now, we'll simplify the expression we obtained in Step 1: $$f(2) = \frac{1}{8+1}$$ $$f(2) = \frac{1}{9}$$ Thus, the value of f(2) is \(\frac{1}{9}\).
03

Finding f(y虏)

Next, we'll find the value of the function f(x) in terms of y虏. Substitute x with y虏 into the function: $$f(y^2) = \frac{1}{(y^2)^3+1}$$
04

Simplifying f(y虏)

Now, we'll simplify the expression we obtained in Step 3: $$f(y^2) = \frac{1}{y^6+1}$$ Thus, the value of f(y虏) is \(\frac{1}{y^6+1}\).

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