Q16. - Algebra 1

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)

$g(-4t)$

Step-by-Step Solution

Answer

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

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 $4\left(4t^2-1\right)$.