Math Problem Statement
- Which among the following functions have an inverse? (a) f(x) = 2x ^ 3 - 5 (b) g(x) = 3x - 8 (c) h(x) = 1/(x ^ 2) (d) k(x) = |x| (0) t(x) = x ^ 2 - 6x 2. Find f(x) = - x ^ 3 + 2
- Find /(x)if f ^ - 1 * (x) = 1/(x - 2)
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Inverse Functions
Cubic Functions
Linear Functions
Quadratic Functions
Absolute Value
Injectivity
Surjectivity
Formulas
f(x) = 2x^3 - 5
f^{-1}(x) = \frac{1}{x - 2}
f(f^{-1}(x)) = x
f(x) = -x^3 + 2
Theorems
Horizontal Line Test
Bijective Functions
Inverse Function Rule
Suitable Grade Level
Grades 10-12
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