Mathematics

Mathematics

Problem

Let f(x)=3x−2f(x)=3x-2 and g(x)=x2−4xg(x)=x^2-4x for all real xx. What is (g∘f)(x)(g\circ f)(x)? a) 9x2−24x+49x^2-24x+4 b) 9x2−12x+49x^2-12x+4 c) 9x2−24x+129x^2-24x+12 d) 9x2−18x+129x^2-18x+12
Intuitive explanation

Function composition means you're plugging one function entirely into another—here, f(x)f(x) becomes the input for gg. The key is to replace every xx in gg's formula with the expression 3x−23x-2, then expand carefully. This transforms an abstract operation into straightforward algebra.

Intuitive explanation

Function composition means you're plugging one function entirely into another—here, f(x)f(x) becomes the input for gg. The key is to replace every xx in gg's formula with the expression 3x−23x-2, then expand carefully. This transforms an abstract operation into straightforward algebra.

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