Studdy AI Logo
Math

QuestionEvaluate (hf)(1)\left(\frac{h}{f}\right)(1) for the functions f(x)=3xf(x)=3x, g(x)=∣x−4∣g(x)=|x-4|, and h(x)=1x−7h(x)=\frac{1}{x-7}.

Studdy Solution

STEP 1

Assumptions1. The functions are defined as follows f(x)=3xf(x)=3x g(x)=∣x−4∣g(x)=|x-4| h(x)=1x−7h(x)=\frac{1}{x-7}. We need to evaluate the function (hf)(1)\left(\frac{h}{f}\right)(1).

STEP 2

The function (hf)(x)\left(\frac{h}{f}\right)(x) is a composition of the functions h(x)h(x) and f(x)f(x), where h(x)h(x) is divided by f(x)f(x). It can be written as(hf)(x)=h(x)f(x)\left(\frac{h}{f}\right)(x) = \frac{h(x)}{f(x)}

STEP 3

Now, we need to substitute x=1x=1 into the functions h(x)h(x) and f(x)f(x).
h(1)=11−7h(1) = \frac{1}{1-7}f(1)=3×1f(1) =3 \times1

STEP 4

Calculate the values of h(1)h(1) and f(1)f(1).
h(1)=11−7=−16h(1) = \frac{1}{1-7} = -\frac{1}{6}f(1)=3×1=3f(1) =3 \times1 =3

STEP 5

Substitute the values of h(1)h(1) and f(1)f(1) into the function (hf)(x)\left(\frac{h}{f}\right)(x).
(hf)(1)=h(1)f(1)=−13\left(\frac{h}{f}\right)(1) = \frac{h(1)}{f(1)} = \frac{-\frac{1}{}}{3}

STEP 6

implify the expression to find the value of (hf)(1)\left(\frac{h}{f}\right)(1).
(hf)(1)=−163=−118\left(\frac{h}{f}\right)(1) = \frac{-\frac{1}{6}}{3} = -\frac{1}{18}So, (hf)(1)=−118\left(\frac{h}{f}\right)(1) = -\frac{1}{18}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord