Problem 10. (7 pts) Given $h(x) = \sqrt{x+3}$ and $j(x) = \frac{x-2}{x^2-9}$, find $(\frac{h}{j})(x)$ and determine the domain of the function $\frac{h}{j}$.
Added by Terri B.
Close
Step 1
$$(\frac{h}{j})(x) = \frac{h(x)}{j(x)} = \frac{\sqrt{x+3}}{\frac{x-2}{x^2-9}} = \frac{\sqrt{x+3}(x^2-9)}{x-2} = \frac{\sqrt{x+3}(x-3)(x+3)}{x-2}$$ Show more…
Show all steps
Your feedback will help us improve your experience
Charles Carter and 77 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
For the functions $f$ and $g$ given, (a) determine the domain of $h(x)=\left(\frac{f}{g}\right)(x)$ and (b) find a new function rule for $h$ in simplified form (if possible), noting the domain restrictions along side. $$f(x)=x^{3}-7 x^{2}+6 x \text { and } g(x)=x-1$$
Relations, Functions, and Graphs
The Algebra and Composition of Functions
For the functions $f$ and $g$ given, (a) determine the domain of $h(x)=\left(\frac{f}{g}\right)(x)$ and (b) find a new function rule for $h$ in simplified form (if possible), noting the domain restrictions along side. $$f(x)=x+3 \text { and } g(x)=x-7$$
For the functions $f$ and $g$ given, (a) determine the domain of $h(x)=\left(\frac{f}{g}\right)(x)$ and (b) find a new function rule for $h$ in simplified form (if possible), noting the domain restrictions along side. $$f(x)=x^{3}-5 x^{2}+2 x-10 \text { and } g(x)=x-5$$
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD