Questions: Determine whether the function is one-to-one. f(x)=6x-8 Is the function one-to-one? Yes No

Solution Steps

A function \( f(x) \) is one-to-one if every output corresponds to exactly one input. In other words, no two different inputs produce the same output. Mathematically, this means that if \( f(a) = f(b) \), then \( a = b \).

To determine whether \( f(x) = 6x - 8 \) is one-to-one, we can use the horizontal line test or algebraically check if \( f(a) = f(b) \) implies \( a = b \).

Let’s use the algebraic method: Assume \( f(a) = f(b) \), then: \[ 6a - 8 = 6b - 8 \] Subtract \(-8\) from both sides: \[ 6a = 6b \] Divide both sides by 6: \[ a = b \] Since \( f(a) = f(b) \) implies \( a = b \), the function is one-to-one.

Final Answer