1. Tardigrade
  2. Question
  3. Mathematics
  4. Let y=f(3 sin x) where x ∈ R and y ∈[-3,5] then domain and range of g(x)=2+3 f(2 x+1) are [a, b] and [c, d] respectively then the value of (a+b+c+d) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $y=f(3 \sin x)$ where $x \in R$ and $y \in[-3,5]$ then domain and range of $g(x)=2+3 f(2 x+1)$ are $[a, b]$ and $[c, d]$ respectively then the value of $(a+b+c+d)$ is equal to

Relations and Functions - Part 2

Solution:

$y=f(t),-3 \leq t \leq 3 \,\,\, \text { and } -9 \leq 3 y \leq 15 $
$-3 \leq 2 x+1 \leq 3 \,\,\, -7 \leq(2+3 y) \leq 17 $
$-2 \leq x<1 \,\,\, -2+1+17-7=9$