Given the functions L(x)=x−2L\left(x\right)=x-2L(x)=x−2 and M(x)=x2M\left(x\right)=x^2M(x)=x2, calculate LM(5)\frac{L}{M}\left(5\right)ML(5)

L M ( 5 ) = 3 25 \frac{L}{M}\left(5\right)=\frac{3}{25} M L ( 5 ) = 25 3

Given the functions L ( x ) = x − 2 L\left(x\right)=x-2 L ( x ) = x − 2 and M ( x ) = x 2 M\left(x\right)=x^2 M ( x ) = x 2 , calculate L M ( 5 ) \frac{L}{M}\left(5\right) M L ( 5 )

Okay. So let's see if we can solve this problem. So in this problem, we are given 2 functions. We're given l of x is equal to x minus 2, and m of x is equal to x squared. We're asked to calculate l over m of 5. Now what this notation is telling us right here is basically we need to take our function l divided by m and then evaluate whatever function we get at 5. So what I'm first going to do is find l over m of x. This is just dividing the 2 functions and getting a general the general function. So in this case, we're going to take our function l, which is x minus 2, and we're going to divide that by our function m, which is x squared. Now at this point, there's not much I can do to simplify this expression, so all I really need to do from here is evaluate this at an x value of 5. So we're going to have l of m of 5, we're going to take this x that we see and replace it with 5. So in this case, we'll have 5 minus 2 divided by 5 squared, and 5 minus 2 is the same thing as 3, and 5 squared is 5 times 5, which is 25. So this right here is the solution to the problem, and that is how you can divide and evaluate functions at certain x values.

Given the functions L ( x ) = x − 2 L\left(x\right)=x-2 L ( x ) = x − 2 and M ( x ) = x 2 M\left(x\right)=x^2 M ( x ) = x 2 , calculate L M ( 5 ) \frac{L}{M}\left(5\right) M L ( 5 )

L M ( 5 ) = 3 25 \frac{L}{M}\left(5\right)=\frac{3}{25} M L ( 5 ) = 25 3

L M ( 5 ) = 25 3 \frac{L}{M}\left(5\right)=\frac{25}{3} M L ( 5 ) = 3 25

L M ( 5 ) = 5 3 \frac{L}{M}\left(5\right)=\frac53 M L ( 5 ) = 3 5

L M ( 5 ) = 3 5 \frac{L}{M}\left(5\right)=\frac35 M L ( 5 ) = 5 3

0. Functions

Combining Functions

Business Calculus

0. Functions

Combining Functions

Struggling with Business Calculus?

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Multiple Choice

Given the functions $L\left(x\right)=x-2$ and $M\left(x\right)=x^2$ , calculate $\frac{L}{M}\left(5\right)$

$\frac{L}{M}\left(5\right)=\frac{25}{3}$

$\frac{L}{M}\left(5\right)=\frac53$

$\frac{L}{M}\left(5\right)=\frac{3}{25}$

$\frac{L}{M}\left(5\right)=\frac35$

Verified step by step guidance

Step 1: Understand the problem. You are given two functions, L(x) = x - 2 and M(x) = x^2, and you are tasked with calculating the value of L/M(5), which is the quotient of L(x) and M(x) evaluated at x = 5.

Step 2: Write the formula for the quotient of two functions. The quotient of L(x) and M(x) is given by (L/M)(x) = L(x) / M(x).

Step 3: Substitute the expressions for L(x) and M(x) into the formula. This gives (L/M)(x) = (x - 2) / (x^2).

Step 4: Evaluate the quotient at x = 5. Substitute x = 5 into the formula: (L/M)(5) = (5 - 2) / (5^2).

Step 5: Simplify the expression. Perform the subtraction in the numerator and the squaring in the denominator to simplify the fraction. The result will be the value of (L/M)(5).

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