Final answer:
To find corresponding inputs or outputs in the function f(x) = 5x² - 4, substitute the given value into the equation and solve. If given an output, set the function equal to that value and solve for x, which may result in two different input values due to the quadratic nature of the function.
Step-by-step explanation:
Given the function f(x) = 5x² - 4, to find corresponding inputs or outputs we simply plug the values into the function. If we are given a specific input (x value), we substitute it into the function to get the output (y or f(x) value). On the other hand, if we are given a specific output and asked to find the input, we would have to solve the equation f(x) = 5x² - 4 for x, which might involve factoring, completing the square, or using the quadratic formula.
For example, if we are asked to find the output when x = 3, we substitute 3 into the function:
f(3) = 5(3)² - 4 = 45 - 4 = 41.
If we are given a function value, say f(x) = 16, and told to find the corresponding input value(s), we set up the equation 5x² - 4 = 16 and solve for x:
- 5x² - 4 = 16
- 5x² = 16 + 4
- 5x² = 20
- x² = 4
- x = ±2
This means the inputs that correspond to the output of 16 are x = 2 and x = -2.