If the function $f$ is defined by $f(x) = 3x + k$ and the function $g$ is defined by $g(x) = \frac{x-1}{3}$, for what value of $k$ is $f(g(x)) = g(f(x))$?
Added by Sofia M.
Close
Step 1
$f(g(x)) = f(\frac{x-1}{3}) = 3(\frac{x-1}{3}) + k = x - 1 + k$ Show more…
Show all steps
Your feedback will help us improve your experience
Ramzi Deek and 59 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
Find the value of the constant $k$ that makes the function continuous. $g(x)=\left\{\begin{array}{ll}{\frac{2 x^{2}-x-15}{x-3}} & {\text { if } x \neq 3} \\ {k x-1} & {\text { if } x=3}\end{array}\right.$
The Derivative
Continuity
In Exercises $25-28$ , find the value of the constant $k$ that makes the function continuous. $$g(x)=\left\{\begin{array}{ll}{\frac{\left(2 x^{2}-3 x-9\right)}{(x-3)}} & {\text { if } x \neq 3} \\ {k x-12} & {\text { if } x=3}\end{array}\right.$$
The function given by $f(x)=k\left(2-x-x^{3}\right)$ has an inverse function, and $f^{-1}(3)=-2 .$ Find $k$.
Functions and Their Graphs
Inverse Functions
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD