The function h(x) is defined to be -4 for all real numbers except 0, where it is defined to be 3.
The function h(x) is defined for all real numbers as follows:
h = {-4 if x≠ 0
{3 if x=0
This piecewise function has two distinct cases based on the value of x. In the first case, when x is not equal to 0, the function returns -4. This implies that for any real number other than 0, the output of the function is a constant value of -4. In mathematical terms:
for h(x)= −4, for x≠ 0
In the second case, when x equals 0, the function returns 3.
This indicates that when the input is specifically 0, the output of the function is 3. In mathematical terms: for h(x)=3, for x=0
To summarize, the function h(x) is defined to be -4 for all real numbers except 0, where it is defined to be 3.
This kind of piecewise definition is common in mathematics and allows for different behaviors of the function in different intervals or for specific values of the input variable.