Let f(x) = sin x and g(x) = ln | x |. If the ranges of the composition functions fog and gof are R1 and R2 respectively, then

Question

Let f(x) = sin x and g(x) = ln | x |. If the ranges of the composition functions fog and gof are R1 and R2 respectively, then (A) R1 = u: -1 le u < 1 R2 = v: - ∞ < v < 0  (B) R1 = u: -∞ < u < 0 R2 = v: -1 le v le 0  (C) R1 = u: -1 < u < 1 R2 = v: - ∞ < v < 0  (D) R1 = u: -1 le u le 1 R2 = v: - ∞ < v le 0

Tardigrade Admin · Accepted Answer

Correct answer is (d) R1 = u: -1 le u le 1 R2 = v: - ∞ < v le 0

Q. Let $f (x) = sin x$ and $g (x)$ = ln | x |. If the ranges of the composition functions fog and gof are $R_{1}$ and $R_{2}$ respectively, then

$R_{1} = {u : - 1 \leq u < 1}, R_{2} = {v : - \infty < v < 0}$

$R_{1} = {u : - \infty < u < 0}$ , $R_{2} = {v : - 1 \leq v \leq 0}$

$R_{1} = {u : - 1 < u < 1}, R_{2} = {v : - \infty < v < 0}$

$R_{1} = {u : - 1 \leq u \leq 1}, R_{2} = {v : - \infty < v \leq 0}$

Correct answer is (d) $R_{1} = {u : - 1 \leq u \leq 1}, R_{2} = {v : - \infty < v \leq 0}$

Q. Let f(x)=sinx and g(x) = ln | x |. If the ranges of the composition functions fog and gof are R1​ and R2​ respectively, then

R1​={u:−1≤u<1},R2​={v:−∞<v<0}

R1​={u:−∞<u<0}, R2​={v:−1≤v≤0}

R1​={u:−1<u<1},R2​={v:−∞<v<0}

R1​={u:−1≤u≤1},R2​={v:−∞<v≤0}