Let f be the function defined as f(x)=x2 in the domain [−7,+7]. The range of f(x) is [a,b]. What is the value of a+b?
To find the range of the function f(x) = x^2 in the domain [−7,+7], we need to determine the minimum and maximum values that the function attains within this domain.
First, let's consider the lowest value in the domain, which is -7. When we plug in -7 into f(x) = x^2, we get f(-7) = (-7)^2 = 49. Therefore, 49 is the smallest value f(x) can take within the domain.
Next, let's consider the highest value in the domain, which is +7. When we plug in +7 into f(x) = x^2, we get f(7) = (7)^2 = 49. Thus, 49 is also the largest value f(x) can take within the given domain.
Hence, the range of f(x) = x^2 in the domain [−7,+7] is [49, 49].
So, the value of a is 49, and the value of b is also 49. Therefore, a + b = 49 + 49 = 98.