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

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 (A) 7 (B) 8 (C) 9 (D) None of these

Tardigrade Admin · Accepted Answer

y=f(t),-3 ≤ t ≤ 3 text and -9 ≤ 3 y ≤ 15 -3 ≤ 2 x+1 ≤ 3 -7 ≤(2+3 y) ≤ 17 -2 ≤ x<1 -2+1+17-7=9

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

7

8

9

None of these

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

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

7

8

9

None of these

y=f(t),−3≤t≤3 and −9≤3y≤15 −3≤2x+1≤3−7≤(2+3y)≤17 −2≤x<1−2+1+17−7=9

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

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