To find the value of x for which f(g(x)) = 0, we first need to understand the given functions: f(x) = x2 – 2x g(x) = 6x + 4 Next, we can substitute g(x) into f(x): f(g(x)) = f(6x + 4) Now, we replace x in the function f(x) with g(x): f(g(x)) = (6x + … Read more
If a number is divisible by both 2 and 3, we can conclude that it is also divisible by 6. This is because 6 is the least common multiple (LCM) of 2 and 3. To understand this better, let’s break it down: Divisibility by 2: A number is divisible by 2 if it is an … Read more
The series presented is a variation of the Fibonacci sequence, which typically starts with 0 and 1, or, as seen here, with 1 and 1. In a standard Fibonacci sequence, each number is the sum of the two preceding ones. Here’s how it breaks down: 1 (1st) 1 (2nd) 2 (1 + 1 = 2, … Read more
Calculating Surface Area and Volume of a Cube A cube is a three-dimensional geometric shape with six equal square faces. To calculate both the surface area and volume, we can use specific formulas based on the length of the edges. Step 1: Calculate Surface Area The formula for the surface area (SA) of a cube … Read more
To find the roots of the function f(x) = x3 + x2 – 6x, we need to set the function equal to zero: x3 + x2 – 6x = 0 The first step is to factor out the common term. Notice that x is a common factor: x(x2 + x – 6) = 0 Now, … Read more
To convert the equation 9x + 10y = 9 into slope-intercept form, we need to rearrange it into the format y = mx + b, where m represents the slope, and b represents the y-intercept. Here are the steps to transform the equation: Start with the original equation: 9x + 10y = 9 Isolate the … Read more
Understanding the Domain of the Square Root Function The square root function is defined as f(x) = √x, and it is important to comprehend that this function only accepts non-negative numbers as inputs. In our scenario, we are examining the function where it is specified that x ≥ 7. This restriction on the domain implies … Read more
The function f(x) = 26x^3 is a cubic polynomial function. To determine the range of a polynomial function, we first analyze the behavior of the function as x approaches positive and negative infinity. As x approaches positive infinity (x → +∞), the term 26x^3 will also approach positive infinity (f(x) → +∞). Conversely, as x … Read more
To convert the polar equation r = 4 sin(θ) into rectangular coordinates, we will use the relationships between polar and rectangular coordinates: x = r cos(θ) y = r sin(θ) r = √(x² + y²) Starting with the polar equation: r = 4 sin(θ) we can express sin(θ) in terms of rectangular coordinates: sin(θ) = … Read more
To solve the quadratic equation 5×2 + 25x = 0, we can start by factoring the equation. First, notice that both terms on the left side are divisible by 5. We can factor out the common factor: 5(x2 + 5x) = 0 Next, we can set the factor inside the parentheses equal to zero: x2 … Read more