# What is the domain and range of g(x)=(1-x^2)?

Mar 1, 2016

domain would be (-infinity to infinity)

Mar 1, 2016

The domain would be unlimited, as there are no 'forbidden' values for $x$ (no fractions, no roots).
Domain $= \left(- \infty , + \infty\right)$

#### Explanation:

For the range we observe that the maximum value of $g \left(x\right)$ happens when $x = 0$ (which means the least to subtract from 1).
Any other value of $x$ would make ${x}^{2} > 0 \to g \left(x\right) < 1$
Range $= \left(- \infty , 1\right]$