Chapter 2.1, Problem 1E

To determine

Find the fill in the blank, if a function $f$ is given by the formula $y=f\left(x\right)$ then $f\left(a\right)$ is the ----- of $f$ at $x=a$

Answer to Problem 1E

Since $y=f\left(x\right)$ we can conclude that $f\left(a\right)$ is the value of the function when $x=a$

Hence the blank must be filled with word ‘value’

Explanation of Solution

Given information: Consider the function $f\left(x\right)=x^3+2x$

Calculation:

For example, evaluate the values of the function $f\left(x\right)=x^3+2x$ for the same values of the variable $x$

Plug the some value $x=-2$ in the function $f\left(x\right)=x^3+2x$ then we get the value of $f\left(-2\right).$

  $\begin{array}{l}f\left(-2\right)={\left(-2\right)}^3+2\left(-2\right)\\ \Rightarrow f\left(-2\right)=-8-4\\ \Rightarrow f\left(-2\right)=-12\end{array}$

This means the valueof $y$ is -12 when $x=-2$

From the above it can be said that the value obtained by replace $x$ by some number $a$ is the value of the function.

Thus, the blank must be filled with word ‘value’