The value of a, if the function f(x) = x + 5, and we are given that f(3a) + 2 = f(2a) + 3 is a = 1.
What is a function?
A function is a relation between a dependent variable and independent variable(s), where every independent variable as input, gives exactly one output for the dependent variable.
How to solve the question?
In the question, we are asked to find the value of a, if the function f(x) = x + 5, and we are given that f(3a) + 2 = f(2a) + 3.
To find the required value of a, we need to solve the given functional equation as follows:
f(3a) + 2 = f(2a) + 3,
or, ((3a) + 5) + 2 = ((2a) + 5) + 3 {Substituting f(3a) = 3a + 5, and f(2a) = 2a + 5, as putting the value inside the parenthesis for f(x) = x + 5, in place of x},
or, 3a + 7 = 2a + 8 {Simplifying},
or, 3a + 7 - 2a - 7 = 2a + 8 - 2a - 7 {Subtracting 2a and 7 from both sides},
or, a = 1.
Thus, the value of a, if the function f(x) = x + 5, and we are given that f(3a) + 2 = f(2a) + 3 is a = 1.
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