Math Problem Statement

F(x)=4x-5 g(x)=(x+4)/5

Solution

You provided two functions:

  1. F(x)=4x5F(x) = 4x - 5
  2. g(x)=x+45g(x) = \frac{x + 4}{5}

Would you like to find specific values, compositions, inverses, or some other property of these functions? Here are some possible directions:

  1. Find the value of F(x)F(x) or g(x)g(x) for a specific xx.
  2. Compute the composition (Fg)(x)(F \circ g)(x) or (gF)(x)(g \circ F)(x).
  3. Determine the inverse functions F1(x)F^{-1}(x) and g1(x)g^{-1}(x).
  4. Analyze the domain and range of F(x)F(x) and g(x)g(x).
  5. Solve the equation F(x)=g(x)F(x) = g(x) for xx.

Tip:

To find the inverse of a function, swap xx and yy and solve for yy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Composition of Functions
Inverse Functions

Formulas

F(x) = 4x - 5
g(x) = (x + 4) / 5
Composition of functions: (F ∘ g)(x)
Inverse functions

Theorems

Theorem of Function Composition
Inverse Function Theorem

Suitable Grade Level

Grades 10-12