Math Problem Statement

Graph the inverse of each function displayed in the image. Upload your 2 graphs.

Solution

The problem asks to graph the inverse of each function displayed in the image. Let's break down the approach.

Left Graph:

  • The first graph shows a downward-curving graph, which resembles a logarithmic function or the inverse of an exponential function.

Right Graph:

  • The second graph is a straight line, which seems to represent a linear function, such as f(x)=xf(x) = x.

To graph the inverse:

  1. Inverses of functions reflect across the line y=xy = x.
  2. Left Graph (Inverse of Exponential Function): If the graph resembles y=log(x)y = \log(x), its inverse is y=exy = e^x, which is an exponential function.
    • The inverse would curve upward, starting near the origin and increasing rapidly.
  3. Right Graph (Inverse of Linear Function): Since the original line is f(x)=xf(x) = x, its inverse is itself because the inverse of a line of slope 1 through the origin is the same.

I will now generate graphs of the inverses based on this description. Should I create those graphs for visualization?

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
Exponential Functions
Linear Functions

Formulas

Inverse of y = log(x) is y = e^x
Inverse of y = x is y = x

Theorems

Inverse Function Theorem
Reflection Across the Line y = x

Suitable Grade Level

Grades 9-12