Questions: Given the function defined by g(x)=3 x^2-6 x+8, find g(a^2). Write your answer in exact, simplified form. g(a^2)=

Transcript text: Given the function defined by $g(x)=3 x^{2}-6 x+8$, find $g\left(a^{2}\right)$. Write your answer in exact, simplified form. \[ g\left(a^{2}\right)= \] $\square$

Solution

Solution Steps

To find $ g(a^2) $, substitute $ a^2 $ into the function $ g(x) = 3x^2 - 6x + 8 $. This involves replacing every instance of $ x $ in the function with $ a^2 $ and simplifying the resulting expression.

Step 1: Substitute $ a^2 $ into the Function

We start with the function defined by $ g(x) = 3x^2 - 6x + 8 $. To find $ g(a^2) $, we substitute $ x $ with $ a^2 $: \[ g(a^2) = 3(a^2)^2 - 6(a^2) + 8 \]

Step 2: Simplify the Expression

Next, we simplify the expression obtained from the substitution: \[ g(a^2) = 3a^4 - 6a^2 + 8 \]