Question

Help please with domain and range :) Picture attached.

Answer 1

The term in the radical can not be negative and the denominator itself can no be zero.

This implies that \(x-6 > 0\implies x>6\). This gives the domain. Note that \(x=6\) is not allowed, because that would make the denominator zero.

Since the square root is always positive and all positive values close to 6 are allowed and as x gets closer to 6 the value of this function, let's call it y, approaches infinity, so \(y> 0\) is the range. Note that \(y=0\) is excluded because as x approaches infinity, y approaches zero but never reaches it.

For both the domain and the range, infinity is not included at the endpoint.

Domain: \((6,\infty)\)
Range: \((0,\infty )\)

https://www.wolframalpha.com/input/?i=plot+1%2Fsqrt%28x-6%29+%2C+6%3Cx%3Cinfinity

Answer 2

thank you so much!