Question

A function for which $f\left(x\right)=f(-x)$for all $x$in the domain of $f$is called a(n) ___ function.

Short answer

A function for which $f\left(x\right)=f(-x)$for all $x$in the domain of $f$ is called an even function.

Step-by-step solution

Step 1. Given information.

We have:

A function for which $f\left(x\right)=f(-x)$ for all x in the domain of $f$ is called a(n) ___ function

Step 2. Fill the blank.

Definition of Even function:

A function such that $f\left(x\right)=f(-x)$where the value remains unchanged if the sign of independent variable is reversed.

Therefore, we get:

A function for which $f\left(x\right)=f(-x)$ for all x in the domain of f is called an even function.