Math Problem Statement

Given f, of, x, equals, minus, x, plus, 1f(x)=−x+1, find f, of, minus, 1f(−1).

Solution

We are given the function f(x)=x+1f(x) = -x + 1, and we are asked to find f(1)f(-1).

Step-by-step process:

  1. Substitute x=1x = -1 into the function f(x)=x+1f(x) = -x + 1:

    f(1)=(1)+1f(-1) = -(-1) + 1

  2. Simplify:

    f(1)=1+1=2f(-1) = 1 + 1 = 2

Thus, f(1)=2f(-1) = 2.

Final Answer:

f(1)=2f(-1) = 2

Would you like further details on this solution or have any questions?

Here are 5 related questions to expand this topic:

  1. What is f(0)f(0) for the function f(x)=x+1f(x) = -x + 1?
  2. How would you find the inverse function of f(x)=x+1f(x) = -x + 1?
  3. What is f(2)f(2) for the same function?
  4. How would you find the domain and range of f(x)=x+1f(x) = -x + 1?
  5. If the function was f(x)=2x+1f(x) = 2x + 1, what would f(1)f(-1) be?

Tip: Always start by substituting the given value into the function before simplifying.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Linear Equations

Formulas

f(x) = -x + 1

Theorems

Substitution Method in Functions

Suitable Grade Level

Grades 6-8