To solve the problem [tex]\( 3 \sin^{-1} x \)[/tex], we start by understanding the components of the expression.
### Step-by-Step Solution:
1. Understand the Function:
- [tex]\(\sin^{-1} x\)[/tex] is the inverse sine function, also known as [tex]\(\arcsin(x)\)[/tex]. This function returns the angle whose sine is [tex]\(x\)[/tex].
2. Scalar Multiplication:
- We need to find the expression for [tex]\(3 \sin^{-1}(x)\)[/tex]. This means multiplying the inverse sine function by 3.
3. Combine the Function with the Scalar:
- We can directly multiply the inverse sine function by 3. Thus, [tex]\(3 \sin^{-1}(x)\)[/tex] becomes [tex]\(3 \arcsin(x)\)[/tex].
### Final Expression:
[tex]\[
3 \sin^{-1} x = 3 \arcsin(x)
\][/tex]
Therefore, the simplified expression for [tex]\(3 \sin^{-1} x\)[/tex] is [tex]\(3 \arcsin(x)\)[/tex].
