Problem

For \(f(x)~=~1/(x~+~3)~-~4\) and \(f^{-1}(x)~=~1/(x~+~4)~-~3\), reflect \(\text{both}~\text{asymptotes}\) and point \((-2,~-3)\) across \(y~=~x\).

Neutral card showing f(x)=1/(x+3)−4 and f⁻¹(x)=1/(x+4)−3, without reflected points, asymptotes, domains, or ranges.

Answer choices

Choose your path.

Preview only

Features: original vertical x=−3 reflects to inverse horizontal y=−3, and original horizontal y=−4 reflects to inverse vertical x=−4. Point (−2,−3) incorrectly remains (−2,−3).

Features: original vertical x=−3 reflects to inverse horizontal y=−3, and original horizontal y=−4 reflects to inverse vertical x=−4. Point (−2,−3) reflects to (−3,−2).

Features: original vertical x=−3 remains inverse vertical x=−3, and original horizontal y=−4 remains inverse horizontal y=−4. Point (−2,−3) reflects to (−3,−2).

Features: original vertical x=−3 reflects to inverse horizontal y=−4, and original horizontal y=−4 reflects to inverse vertical x=−3. Point (−2,−3) reflects to (−3,−2).

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

For \(f(x)~=~1/(x~+~3)~-~4\) and \(f^{-1}(x)~=~1/(x~+~4)~-~3\), reflect \(\text{both}~\text{asymptotes}\) and point \((-2,~-3)\) across \(y~=~x\).

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.