Question

The range of the function $\left(f\right(x)=9-7\sin x)$ is

• A. $(2,16)$
• B. $[2,16]$
• C. $[-1,1]$
• D. $(2,16]$

Answer 1

Answer: (A), (B)

$(2,16)$
$[2,16]$

Given the function $f\left(x\right)=9-7\sin x$.

Let $y=f\left(x\right)$.

Now,

$y=9-7\sin x$

or, $\sin x=\frac{9-y}{7}$.

We've,

$-1\le \sin x\le 1$, $\forall x\in R$

or, $-1\le \frac{9-y}{7}\le 1$

or, $-7\le 9-y\le 7$

or, $-16\le -y\le -2$

or, $2\le y\le 16$.

So range is $[2,16]$ also $(2,16)$ be a subset of the range of the function.