If f(x) = √(x+12) and g(x) = 2 - √x, what is the value of (f-g)(144)?
Answer (2)
Find the expression for ( f − g ) ( x ) by subtracting g ( x ) from f ( x ) : ( f − g ) ( x ) = f ( x ) − g ( x ) = 2 x + 10 .
Substitute x = 144 into the expression: ( f − g ) ( 144 ) = 2 144 + 10 .
Calculate the square root and simplify: ( f − g ) ( 144 ) = 2 ( 12 ) + 10 .
Evaluate the expression to find the final answer: ( f − g ) ( 144 ) = 34 , so the answer is 34 .
Explanation
Understanding the Problem We are given two functions, f ( x ) = x + 12 and g ( x ) = 2 − x . We need to find the value of ( f − g ) ( 144 ) . This means we need to subtract the function g ( x ) from the function f ( x ) and then evaluate the resulting function at x = 144 .
Finding the Expression for (f-g)(x) First, let's find the expression for ( f − g ) ( x ) . This is done by subtracting g ( x ) from f ( x ) :
( f − g ) ( x ) = f ( x ) − g ( x ) = ( x + 12 ) − ( 2 − x )
Simplify the expression by combining like terms:
( f − g ) ( x ) = x + 12 − 2 + x = 2 x + 10
Substituting x = 144 Now, we need to evaluate ( f − g ) ( 144 ) . Substitute x = 144 into the expression we found:
( f − g ) ( 144 ) = 2 144 + 10
We know that 144 = 12 , so substitute that in:
( f − g ) ( 144 ) = 2 ( 12 ) + 10
Evaluating the Expression Now, perform the calculation:
( f − g ) ( 144 ) = 24 + 10 = 34
So, the value of ( f − g ) ( 144 ) is 34.
Examples
Imagine you are analyzing the profit of two different products. Let's say f(x) represents the revenue from selling x units of product A, and g(x) represents the cost of producing x units of product A. Then (f-g)(x) would represent the profit from selling x units of product A. If you want to know the profit from selling 144 units, you would calculate (f-g)(144). This concept is useful in business to determine profitability and make informed decisions about production and sales.
To find ( f − g ) ( 144 ) , we subtract the two functions and evaluate at x = 144 . This yields approximately 22.49 .
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