Chapter 1.7, Problem 61PPE

To determine

The value of the expression $3\left[f\left(1\right)\right]+2$ if $f\left(t\right)=2t^3$ .

Answer to Problem 61PPE

The value of the expression $3\left[f\left(1\right)\right]+2$ if $f\left(t\right)=2t^3$ is $8$ .

Explanation of Solution

Given:

The expression is $f\left(t\right)=2t^3$ .

Calculation:

Substitute $1$ for $t$ in the expression $f\left(t\right)=2t^3$ as follows:

  $\begin{array}{c}f\left(1\right)=2\times 1^3\\ =2\times 1\\ =2\end{array}$

Substitute $f\left(1\right)=2$ in expression $3\left[f\left(1\right)\right]+2$ as follows:

  $\begin{array}{c}3\left[f\left(1\right)\right]+2=3\left[2\right]+2\\ =6+2\\ =8\end{array}$

Thus, the value of the expression $3\left[f\left(1\right)\right]+2$ if $f\left(t\right)=2t^3$ is $8$ .