Question

If f(x) is a continuous function defined for all real numbers, f(–10) = –2, f(–8) = 5, and f(x) = 0 for one and only one value of x, then which of the following could be that x value?

–7
–9
0
2

Answer 1

f(-10)=-2, f(-8)=5, and f is continuous. All these mean that f(x) is 0 for x in between -10 and -8.

That is, f at -10 is negative, then at -8 is positive. So the graph of f "cuts" the x-axis for an x value in (-10, -8).

Since there is only one value such that f(x)=0, x can only be -9.


Answer: -9