Functions: The Basics, Composites, and Inverse Functions

The video tutorial covers the function F, explaining how to substitute values into it and find F(-7). It then demonstrates how to express the inverse of function F. The tutorial proceeds to introduce function G and shows how to calculate the composite function FG(3). Finally, it discusses domain restrictions for function G, emphasizing the importance of avoiding negative values under the root symbol.

What is the result of substituting -7 into the function F(x) = (3x - 5) / 4?

• -21/4

• -26/4

• -13/2

• -6.5

How do you express the inverse of the function F(x) = (3x - 5) / 4?

• F^-1(x) = (3x - 5) / 4

• F^-1(x) = (3x + 5) / 4

• F^-1(x) = (4x - 5) / 3

• F^-1(x) = (4x + 5) / 3

What is the first step in finding FG(3) when G(x) = √(19 - x)?

• Multiply F and G

• Find the inverse of G

• Substitute 3 into the G function

• Substitute 3 into the F function

What is the value of G(3) when G(x) = √(19 - x)?

• 4

• 16

• 3

• 19

What is the final result of FG(3) when F(x) = (3x - 5) / 4 and G(x) = √(19 - x)?

• 7/4

• 5/4

• 4

• 3

Which values of X cannot be included in the domain of G(x) = √(19 - x)?

• X ≤ 19

• X = 19

• X < 19

• X > 19

Why can't values greater than 19 be included in the domain of G(x) = √(19 - x)?

• They result in a negative under the square root

• They make the function undefined

• They make the function linear

• They result in a zero under the square root