Wolfram Research

Function Repository Resource:

EvenFunctionQ

Source Notebook

Determine whether an expression is an even function of the given variable or variables

Contributed by: Wolfram|Alpha Math Team

EvenQ[f[x],x]

returns True if f[x] is an even function of x, and returns False otherwise.

Examples

Basic Examples

Test whether a basic power function is even:

In[1]:=
ResourceFunction["EvenFunctionQ"][x^2, x]
Out[1]=

Test another power function:

In[2]:=
ResourceFunction["EvenFunctionQ"][x^3, x]
Out[2]=

Test whether a constant function is even:

In[3]:=
ResourceFunction["EvenFunctionQ"][1, x]
Out[3]=

Test whether the absolute value function is even:

In[4]:=
ResourceFunction["EvenFunctionQ"][Abs[x], x]
Out[4]=

Test whether the sine function is even:

In[5]:=
ResourceFunction["EvenFunctionQ"][Sin[x], x]
Out[5]=

Test whether the cosine function is even:

In[6]:=
ResourceFunction["EvenFunctionQ"][Cos[x], x]
Out[6]=

Test whether a Gaussian function is even:

In[7]:=
ResourceFunction["EvenFunctionQ"][Exp[-x^2], x]
Out[7]=

Test a signed Gaussian function:

In[8]:=
ResourceFunction["EvenFunctionQ"][Sign[x] Exp[-x^2], x]
Out[8]=

Test whether a hyperbolic sine function of two variables is even:

In[9]:=
ResourceFunction["EvenFunctionQ"][Sinh[x + y], {x, y}]
Out[9]=

Test whether the hyperbolic tangent function is even:

In[10]:=
ResourceFunction["EvenFunctionQ"][Tanh[x], x]
Out[10]=

Test whether the error function is even:

In[11]:=
ResourceFunction["EvenFunctionQ"][Erf[x], x]
Out[11]=

Test whether a Fresnel integral is even:

In[12]:=
ResourceFunction["EvenFunctionQ"][FresnelC[x], x]
Out[12]=

Test whether a shifted Fresnel integral is even:

In[13]:=
ResourceFunction["EvenFunctionQ"][FresnelC[x] + 1, x]
Out[13]=

Resource History

See Also

License Information