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Published on October 13, 2025
Determine if F(x)=4x-2 and G(x)=(-2+x)/4 are inverse functions by composing them. The composition F(G(x)) resulted in x-4 and G(F(x)) resulted in x-1, neither of which is x, so they are not inverses.
Determine if the following are inverses using a composition of functions F(x)=7x+3 and g(x)=x-3 over 7
The expression evaluates to 0 after calculating the numerator and denominator separately and then dividing them.
The provided text contains a series of math problems, including algebraic expressions, exponents, fractions, and polynomial operations. The solutions demonstrate various techniques for simplifying and manipulating these expressions, such as factoring, expanding, and applying the rules of exponents and fractions.
The expression 3³ ÷ 3 ÷ 3 simplifies to 1.
24 is 60 percent of 40.
The difference of squares formula is used to evaluate the expression 100^2 - 99^2, resulting in 199.
To find the smallest possible values for A and B in a 10-digit number divisible by both 8 and 9, the last three digits (9B8) must be divisible by 8, and the sum of all digits must be divisible by 9. This leads to B=2 and A=3 as the smallest possible values.
To find 2^(m+n), solve for m and n in the equations 2^m = 1 and 2^n = 16, then substitute the values into the expression.
The expression 0^0 is considered an indeterminate form in calculus because different approaches to evaluating it yield different potential values. While some approaches suggest a value of 1 and others suggest 0, the limit does not have a single, well-defined value. In some contexts, like combinatorics, it is defined as 1 for convenience.
The magnitude of the given row vector is calculated, resulting in 3.
The provided document details the simplification of algebraic fractions and the solution of algebraic expressions. Part 1 simplifies various rational expressions by factoring the numerators and denominators, canceling common factors. Part 2 involves adding, subtracting, and multiplying rational expressions, often requiring finding common denominators and simplifying the resulting expressions.