# Solving Functions

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An algebraic function f(x) is written in terms of variables, coefficients and constants. The condition for solving the functions in p(x)/q(x) form is the denominator cannot be equal to zero i.e. q(x) ≠ 0. The function can be solved or simplified using different mathematical properties such as multiplicative property, associative property, additive inverse multiplicative inverse and many more. The function f(x) can be assigned different values of x.

Example 1: Solve the given function and find the value of x.
If f(x) = 7x/ (2x + 10) if f(x) = 1   .

Solution: Given is the function f(x) = 5x/(x + 12) and f(x) = 1.
7x / (2x + 10) = 1
Multiplying (x + 10) both sides of the equation.
(x + 10) [7x / (2x + 10)] = 1 (x + 10); 7x = 2x + 10.
Subtract both sides of the equation with 2x; 5x = 10
Divide by 5 on both sides of the equation.
5x/ 5 = 10/ 5;
Hence solution is x = 2.

Example 2: Solve the given function and find the value of x.
If f(x) = (7x – 21)/3x if f(x) = 0.

Solution: Given is the function f(x) = (7x – 21)/3x for f(x) = 0.
(7x – 21)/3x =0
Multiplying 3x both sides of the equation; (7x – 21) = 0
Add both sides of the equation with 21; 7 x = 21.
Divide by 7 on both sides of the equation; 7x/ 7 = 21/ 7; x = 3.
Hence solution is x = 3.