Question

Examples 4 and 5 If$f\left(x\right)=6x+7$ and$g\left(x\right)=x^2-4,$ find each value. (P. 49)

$g(-4t)$

Short answer

The function value at$x=-4t$ is$4\left(4t^2-1\right)$.

Step-by-step solution

Step 1. Interpreting of function.

$g\left(-4t\right)$Indicates the value of function$g\left(x\right)$ at$x=-4t$

Step 2. Apply substitution method.

Substitute$x=-4t$ into the function$g\left(x\right)$

Step 3. Calculation.

The function value at$x=-4t$ is calculated as follows:

$\begin{array}{l}g\left(-4t\right)={\left(-4t\right)}^2-4\\ g\left(-4t\right)=16t^2-4\\ g\left(-4t\right)=4\left(4t^2-1\right)\end{array}$

Thus, the function value at$x=-4t$ is$4\left(4t^2-1\right)$.