1. Tardigrade
  2. Question
  3. Mathematics
  4. If domain of f(x) is [-1,4], then number of integers in the domain of g(x)=f(2-√x)+f(1-x(1/3)) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If domain of $f(x)$ is $[-1,4]$, then number of integers in the domain of $g(x)=f(2-\sqrt{x})+f\left(1-x^{\frac{1}{3}}\right)$ is

Relations and Functions - Part 2

Solution:

$-1 \leq 2-\sqrt{x} \leq 4 \Rightarrow-3 \leq-\sqrt{x} \leq 2 \Rightarrow-2 \leq \sqrt{x} \leq 3 \Rightarrow 0 \leq x \leq 9$.....(1)
$-1 \leq 1- x ^{\frac{1}{3}} \leq 4 \Rightarrow-2 \leq- x ^{\frac{1}{3}} \leq 3 \Rightarrow-3 \leq x ^{\frac{1}{3}} \leq 2 \Rightarrow-27 \leq x \leq 8$.....(2)
Intersection of (1) \& (2) is $0 \leq x \leq 8$
$\therefore$ Number of integers $=9$