Function Composition and Domain Analysis

Anil Kumar explains how to find the composite function G of F, given two functions f(x) and g(x). He details the steps to determine the domain and range of G of F, emphasizing the restrictions imposed by the domain of f(x). The video concludes with a visualization of the function, highlighting its semicircular nature due to the square root operations involved.

Who is the video dedicated to?

• Composite Functions

• YouTube

• Alexander

• Anil Kumar

What is the main problem discussed in the video?

• Finding the derivative

• Solving quadratic equations

• Graphing linear functions

• Understanding range of composite functions

What is the expression for f(x)?

• Square root of 4 minus x squared

• Square root of 5 plus x squared

• x squared minus 4

• 5 plus x squared

What is the expression for g(x)?

• Square root of 4 minus x squared

• Square root of 5 plus x squared

• x squared minus 4

• 5 plus x squared

What is the domain of the function g(x)?

• x is between -3 and 3

• x is less than 0

• x is between -2 and 2

• x is greater than 0

What is the range of the function g(x)?

• y is between -5 and 5

• y is between -3 and 3

• y is between 0 and 5

• y is between 0 and 3

What is the result of substituting x = 0 in g(x)?

• 3

• 0

• Square root of 5

• 2

What is the result of substituting x = ±2 in g(x)?

• 3

• Square root of 5

• 2

• 0

What does g(f(x)) represent?

• Square root of 9 minus x squared

• Square root of 5 plus x squared

• Square root of 4 minus x squared

• Square root of 5 plus square of square root of 4 minus x squared

What is the simplified form of g(f(x))?

• Square root of 5 plus x squared

• x squared minus 9

• Square root of 9 minus x squared

• Square root of 4 minus x squared