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 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

3. Functions

Function Operations

College Algebra

3. Functions

Function Operations

Struggling with College Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

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

First, understand the functions given: L(x) = x - 2 and M(x) = x^2. These are the functions you will use to calculate LM(5), \frac{L}{M}(5), and ML(5).

To find LM(5), calculate L(5) and M(5) separately. Substitute x = 5 into L(x) to get L(5) = 5 - 2. Then substitute x = 5 into M(x) to get M(5) = 5^2.

Once you have L(5) and M(5), multiply these values together to find LM(5).

For \frac{L}{M}(5), use the values of L(5) and M(5) calculated earlier. Divide L(5) by M(5) to find \frac{L}{M}(5).

To find ML(5), multiply M(5) by L(5) using the values calculated earlier. This is similar to LM(5) but in reverse order.

5:56m

Watch next

Master Adding & Subtracting Functions with a bite sized video explanation from Patrick

Start learning

Function Operations practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice