In Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. ƒ¹ (1)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. In this case, we need to evaluate the inverse function ƒ¹(1), which means finding the value of x such that f(x) equals 1. Understanding how to evaluate functions is crucial for solving problems related to function inverses.

Inverse Functions

An inverse function reverses the effect of the original function. For a function f(x), its inverse f¹(y) satisfies the equation f(f¹(y)) = y. To find ƒ¹(1), we need to determine which input x in the function f(x) = 2x - 5 results in an output of 1, highlighting the relationship between a function and its inverse.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. In this context, we need to solve the equation 2x - 5 = 1 to find the corresponding x value for ƒ¹(1). Mastery of solving linear equations is essential for evaluating functions and their inverses effectively.