Question

lf a function $f\left(x\right)$ is defined for $x\in [0,1]$, then the function $f(2x+3)$ is defined for

• A. $x\in [0,1]$
• B. $x\in [-\frac{3}{2},-1]$
• C. $x\in R$
• D. $x\in [-\frac{3}{2},1]$

Answer 1

The correct option is B $x\in [-\frac{3}{2},-1]$

Since $f\left(x\right)$ is defined for $x\in [0,1]$. Therefore,
$f(2x+3)$ exists if $0\le 2x+3\le 1\Rightarrow -\frac{3}{2}\le x\le -1\Rightarrow$
$x\in [-\frac{3}{2},-1]$