HardMathematicsHigh School (11–12)Functions and Calculus › Graphs of FunctionsNumericalBoard Exam

Write f(x) = (x - 2)³ as the sum of an even function and an odd function.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Write $f(x) = (x - 2)^3$ as the sum of an even function and an odd function.

Need a reminder? The key ideaShow

$f(x - h) + k$ moves the graph $h$ right and $k$ up; $a\,f(x)$ stretches the heights; $f(-x)$ and $-f(x)$ reflect it. Even: $f(-x) = f(x)$ . Odd: $f(-x) = -f(x)$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← Show that {x} = x - [x] has period 1. Then find the period of {5x}.Let f(x) = x + 5 and g(x) = 4x - 1. Find (g ° f)(x) and (f ° g)(x), and their values at x = 3. →

More onFunctions and Calculus › Graphs of Functions

Discussion (0)

Loading…

Write f(x) = (x - 2)³ as the sum of an even function and an odd function.

The worked solution

Discussion (0)

Want to go further in Functions and Calculus › Graphs of Functions?