Simplifying Expressions and Functions

The video tutorial explains how to evaluate a function by substituting a given expression into it. The process involves substituting 2x into the function f(x) = 2x^2 - 7, simplifying the expression, and arriving at the final result, f(2x) = 8x^2 - 7. The tutorial provides step-by-step guidance and encourages students to try solving the problem independently.

What is the initial function given in the problem?

• f(x) = x^2 - 7

• f(x) = 2x^2 + 7

• f(x) = 2x + 7

• f(x) = 2x^2 - 7

What is the first step suggested to solve the problem?

• Simplify the function

• Substitute 2x for x in the function

• Find the derivative

• Integrate the function

What should you substitute into the function?

• 2x

• 7

• 2

• x

After substitution, what does the function become?

• f(2x) = 2(2x)^2 - 7

• f(2x) = 2x^2 - 7

• f(2x) = 4x^2 - 7

• f(2x) = 8x^2 - 7

What is the next step after substituting 2x into the function?

• Add 7 to the function

• Simplify the expression

• Multiply by 2

• Divide by 2

What is the result of simplifying 2(2x)^2?

• 4x^2

• 8x^2

• 16x^2

• 2x^2

What is the final simplified form of f(2x)?

• f(2x) = 4x^2 - 7

• f(2x) = 4x^2 + 7

• f(2x) = 8x^2 - 7

• f(2x) = 8x^2 + 7

What operation is performed on 2 and 4x^2 in the final step?

• Division

• Multiplication

• Subtraction

• Addition

What is the coefficient of x^2 in the final answer?

• 16

• 8

• 4

• 2

What remains unchanged in the function after simplification?

• The variable x

• The exponent of x

• The constant term

• The coefficient of x^2