Question

Find the range of the function $f\left(x\right)=\frac{1}{x}+2$.

• A. All real numbers
• B. All real numbers except $-\frac{1}{2}$
• C. All real numbers except $0$
• D. All real numbers except $2$
• E. All real numbers between $2$ and $3$

Answer 1

Answer: (D)

All real numbers except $2$

Given: $f\left(x\right)=\frac{1}{x}+2$

Isolate $x$: First subtract $2$ from both the sides to get

$y-2=\frac{1}{x}$

$x=\frac{1}{y-2}$

The above equation showsthat for any $y$ value other than $2$, there is an $x$ value.

Therefore, the range of the function defined by $f\left(x\right)=\frac{1}{x}+2$ as all real numbers except $2$.