How to solve Functions

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Suppose X and Y are two non-empty sets of real numbers. If there exists a definite rule f which associates each element x of X with a unique element y of Y, then the rule f is called a function or mapping of X into Y and it is denoted by the symbol
if: x → y ( read as, f maps X into Y).
 
The element of the set Y corresponding to the element x of X obtained by the rule f is denoted by f(x). Thus,
if the rule f determines y € Y when x € X then we shall have,
y = f(x)

Example: - If f(x-2) = 2x + 5, then find the value of f(x).
Solution: -     f(x-2) = 2x + 5                        … (1)
Replacing x by (x + 2) in (1) we get,
f (x + 2 – 2) = 2 (x +2) + 5
f (x) = 2 x + 4 + 5
f (x) = 2 x + 9
Therefore f (x) = 2 x + 9

Question 2: - If f (x) = 2 x^2 + 3 x + 9, then find the value of f (-1).
Solution: - f (x) = 2 x^2 + 3 x + 9    … (1)
Substituting x = -1 in equation (1) we get,
F (-1) = 2 (-1)^2 + 3 (-1) +9
F (-1) = 2 * 1 – 3 + 9
F (-1) = 2 + 6 = 8
Therefore f(-1) = 8

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