Find the range of the function f(x)=10-x squared

Answer:I'll assume x is squared, case in which the function looks like this:[tex]f(x) = 10-x^{2}[/tex]The range is (-∞; 10] and be careful at those parenthesesStep-by-step explanation:You could, for example, think of what happens to x for different situations.If x is very big, [tex]x^{2}[/tex] is even bigger. 10 - [tex]x^{2}[/tex] thus gets smaller, because you're subtracting something bigger and bigger. So, it tends to negative infinity.Now, if x is any bigger than 10, it'll be a negative result, so x>10 ==> f(x)<0actually, this happens for any x>[tex]\sqrt{10}[/tex]For x negative, smaller (more negative) than -[tex]\sqrt{10}[/tex], the result is the same.If x is in the range [tex]-\sqrt{10}; \sqrt{10}[/tex] then the result becomes positive, since we're subtracting something smaller than 10. The biggest result we could ever achieve is when x=0. Thus 10 - 0 = 10. In conclusion, 10 is the "upper limit" and -∞ is the "lower limit".Thus, the range is (-∞ ; 10] AND BE CAREFUL AT PARENTHESES.