Inverse Powers and Radical Functions
Read this topicExplanations 3
- Powers and Radicals We're going to think about the relationship between power functions and radical functions/radical expressions. The key point in this relationship is that the…
By Jonathan Heller, Anusha Rahman
- (Video) Finding the Inverse Function (Exponent and Radical) by MATHStorya In this video by MATHStorya, you will learn how to find the inverse of a function, with both radicals a…
By Anusha Rahman
- Inverse Powers and Radical Functions In this lesson, we are going to explore inverse powers and radical functions. These are different ways to write and work with powers and roo…
By Anusha Rahman
Problems 10
- Find a non-zero fractional solution, x=p/qx=p/qx=p/q (in lowest terms), to the equation (3x)6=(6x)3(3x)^6 = (6x)^3(3x)6=(6x)3. What is 10p+q10p+q10p+q?
- Let f(x)=x+3f(x) = \sqrt{x}+3f(x)=x+3 for all x≥0x \ge 0x≥0. What is the domain of f−1f^{-1}f−1 (where f−1f^{-1}f−1 is the function which satisfies f(f−1(x))=xf(f^{-1}(x)) = xf…
- If f(x)=4−x−23f(x)=4-\sqrt[3]{x-2}f(x)=4−3x−2, evaluate: f(−2),f(−1),f(0),f(1), and f(2)f(-2), f(-1), f(0), f(1),\;\mathrm{and}\;f(2)f(−2),f(−1),f(0),f(1),andf(2) to the neares…
- Find the inverse of f(x)=x3f(x)=x^3f(x)=x3.
- Find the inverse of f(x)=8x4f(x)=8x^4f(x)=8x4.
- Find the inverse of f(x)=x13f(x)=x^{\frac13}f(x)=x31.
- Find the inverse of f(x)=0.07x34f(x)=0.07x^{\frac34}f(x)=0.07x43.
- Let f(x)=0.42xaf(x)=0.42x^af(x)=0.42xa where aaa is a nonzero real number. Find aaa if f−1(x)=7.889x1af^{-1}(x)=7.889x^{\frac1a}f−1(x)=7.889xa1.
- Let f(x)=12x2f(x)=12x^2f(x)=12x2. Find f(x)f−1(x)f(x)f^{-1}(x)f(x)f−1(x) for x>0x>0x>0.
- True or False\text{True or False}True or False === If f(x)=axbf(x)=ax^bf(x)=axb and f−1(x)=(1a)1bx1bf^{-1}(x)=(\frac1a)^{\frac1b}x^{\frac1b}f−1(x)=(a1)b1xb1 where aaa and bbb…