Home › TS EAMCET › Mathematics › Limits and Continuity › For f(x) = x³ + x − 1, in which interval must a …
For f(x) = x³ + x − 1, in which interval must a root lie?
A(2, 3)
B(−2, −1)
C(0, 1)
D(1, 2)
Answer & Solution
Correct answer: C. (0, 1)
f is continuous with f(0) = −1 and f(1) = 1, so a root lies between 0 and 1.
Related questions
How many real points of discontinuity does (x + 1)/(x² − 5x + 6) have?Let f(x) = 2x + 1 for x < 2 and x² + 1 for x ≥ 2. What is the limit at x = 2?What does the differentiability of a function at a point guarantee about it there?How many points in the open interval (0, 3) is ⌊x⌋ discontinuous at?At which of these points is tan x discontinuous?At which real number does f(x) = 1/(x − 3) break down?Define f(x) = (1 − cos x)/x² off zero. Continuity at 0 needs f(0) equal to what?Take f = kx² when x ≤ 2 and f = 3 when x > 2. Continuity at 2 forces k to be what?