Questions: For x ≠ 0, if f(x)=3x^2 and g(x)=1/x, then f(g(x))= - 3x - 1/(3x^2) - 3/x^2 - x^2/3 - 1/(3x)

Solution Steps

To solve for \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \). Given \( f(x) = 3x^2 \) and \( g(x) = \frac{1}{x} \), we substitute \( g(x) \) into \( f(x) \) to get \( f\left(\frac{1}{x}\right) \). This involves replacing \( x \) in \( f(x) \) with \( \frac{1}{x} \) and simplifying the expression.

We are given two functions:

• \( f(x) = 3x^2 \)
• \( g(x) = \frac{1}{x} \)

To find \( f(g(x)) \), we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f\left(\frac{1}{x}\right) = 3\left(\frac{1}{x}\right)^2 \]

Now we simplify the expression: \[ f(g(x)) = 3 \cdot \frac{1}{x^2} = \frac{3}{x^2} \]

Final Answer