Inverses of Power Functions Are Power Functions
Read this topicExplanations 2
- Power Function Inverses The big takeaway for this section is exactly what the title says: inverse of power functions are power functions. There is a generalized process to show …
By Jonathan Heller, Sylvia Freeman
- So how, exactly, do we find the inverse of a power function? You might remember our trick for finding inverses algebraically. But I'll recap now. Say we have a function y=f(x).y…
By Joshua Siktar
Problems 22
- What is the inverse of the following function? f(x)=5x−125f(x)=\sqrt[5]{5x-12}f(x)=55x−12
- What is the inverse of the following function? f(x)=x3+6f(x)=x^3+6f(x)=x3+6
- What is the inverse of the following function? f(x)=2x+87f(x)=\sqrt[7]{2x+8}f(x)=72x+8
- What is the inverse of the following function? f(x)=5(x−3)5+19f(x)=5(x-3)^5+19f(x)=5(x−3)5+19
- What is the inverse of the following function? f(x)=−2x14f(x)=-2x^{\frac{1}{4}}f(x)=−2x41
- What is the inverse of the following function? f(x)=−14x−3f(x)=-\frac{1}{4}x^{-3}f(x)=−41x−3
- Match the following function with the graph of its inverse. f(x)=x3f(x)=x^3f(x)=x3
- Match the following function with the graph of its inverse. f(x)=x2f(x)=x^2f(x)=x2
- Match the following function with the graph of its inverse. f(x)=x3+1f(x)=\sqrt[3]{x}+1f(x)=3x+1
- Match the following function with the graph of its inverse. f(x)=x−75f(x)=\sqrt[5]{x-7}f(x)=5x−7
- What is the inverse of y=x2y=x^2y=x2 on the domain (−∞,∞)?(-\infty, \infty)?(−∞,∞)?
- Which of the following graphed power functions have an inverse?
- Kelsey thinks that the height of any tree can be measured by the function h(x)=112x3h(x)=\frac{1}{12}x^{3}h(x)=121x3 where xxx is the length in inches of any branch on a tree. …
- The Wi-Fi at school slows down when more people are using their laptops. The Wi-Fi speed can be modeled by the function f(x)=12x12+100f(x)=\frac{1}{2}x^{\frac{1}{2}}+100f(x)=21…
- True or False\text{True or False}True or False === The power 13\frac{1}{3}31 is the same as the cubed root. (x3=x13)(\sqrt[3]{x}=x^{\frac{1}{3}})(3x=x31).
- True or False\text{True or False}True or False === The inverse function for (x)57(x)^{\frac{5}{7}}(x)75 is x75\sqrt[7]{x}^{5}7x5.
- Which colored functions above have power inverses?
- What is the inverse of the graphed function above?
- What is the inverse of the function f(x)=(x−2)8+12?f(x)= (x-2)^8+\frac{1}{2}?f(x)=(x−2)8+21?
- Which of the colored functions above are the inverse to the purple function f(x)=xf(x)=\sqrt{x}f(x)=x?
- Let fff and ggg be invertible functions such that f(x)=2g(x).f(x) = 2^{g(x)}.f(x)=2g(x). Which of the following is true?
- If f(x)=(2x)xf(x) = (2^x)^xf(x)=(2x)x on the domain x∈[1,∞),x \in [1, \infty),x∈[1,∞), what is the inverse f−1(x)?f^{-1}(x)?f−1(x)?