Question

the function f is defined by f(x)=3x² +2. find f(3x). f(3x) =

Explanation:

Step1: Substitute \(3x\) into \(f(x)\)

Given \(f(x) = 3x^2 + 2\), replace \(x\) with \(3x\). So we get \(f(3x)=3(3x)^2 + 2\).

Step2: Simplify \((3x)^2\)

Using the exponent rule \((ab)^n=a^n b^n\), \((3x)^2 = 3^2\times x^2=9x^2\). Then \(3(3x)^2=3\times9x^2 = 27x^2\).

Step3: Combine terms

So \(f(3x)=27x^2 + 2\).

Answer:

\(27x^2 + 2\)