In reference to the function: g(x)=x^2 +2x−6 (−1 ≤ x ≤ 3) Show that the inverse function g−1 has the rule g-1 (x) = √(x + 7) - 1  justifying each step clearly and also giving its domain and image set.

Q: Find the domain of the function g(x) =√(x - 2)/(x - 5)

A: We can not have negative number inside the square root. x-2≥0 So, x≥2

Q: Show that f(x) = (3x - 2) / (5x - 3) , is its own inverse ?

A:

Q: Let f (x) = -3 (x – 5) (x + 2) Let 8 (x) be represented by the graph below. Which statement is true…

A:

Q: Let f(x) = 12 - 4x°. Find the inverse and verify your result. 3.

A:

Q: What is the inverse of the function f(x) = In (5x + 1) - 7?

A: Given query is to find the inverse of the function f(x).

Q: Find f(a), f(a+h), and the difference quotient for the function given below.

A:

Q: Explain why both f (x) = x/ (1- x4) and g(x) = p are algebraic g(x) = -x / √(1-x4) functions.

A: f(x)=x1-x4 and g(x)=-x1-x4

Q: For the function f defined by f(x) = x2 - 4x + 1, find: f(-x)

A: Here given as fx=x2-4x+1

Q: If the point in function f(x) has the coordinates (-2, 4), then what would be the coordinate for…

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Q: Consider the function f defined by f(x) = (3 – x)(4 + 3x). What is f(-3)?

A: Given  f(x)=(3-x)(4+3x)

Q: Explain why the domain of f(x) = x2 + k must be restricted to find an inverse function.

A: Given: