Evaluating Functions

A function is a mapping between an input and output. For example, the function f(x) = 3x – 2 takes an input ‘x’ and output is 3x – 2.

In other words, we can say that a function is a relation between two variables, in such a way that value of the first variable gives one and only one value for the second variable.

Value of f(x) = 3x – 2 at x = 3 is f(3) = 3(3) – 2 = 9 – 2 = 7

Example: If g(x) = 2x + 1, then what is the value of g(-3)?

g(-3) = 2(-3) + 1 = -6 + 1 = -5

Example: If f(x) = -5x² + 7, the find f(4).

f(4) = -5(4)² + 7 = -5(16) + 7 = -80 + 7 = -73

CHECK POINT

1. If f(x) = -7^2x, then find f(2).
2. If h(n) = 2 × 5^{(n – 3)}, then what is the value of h(4)?
3. If f(x) = x³ – 1, the find x if f(x) = 215.
4. If g(t) = 2t² – 1, then what is the value of g(5)?
5. If f(t) = 5t – 1, the find f(-5).