Studdy AI Logo
Math  /  Algebra

QuestionGiven f(x)=14x+5f(x)=\frac{14}{x+5}, find (f∘f)(1)(f \circ f)(1) (f∘f)(1)=(f \circ f)(1)= □\square (Type an integer or a fraction. Simplify your answer.)

Studdy Solution

STEP 1

1. We are given the function f(x)=14x+5 f(x) = \frac{14}{x+5} .
2. We need to find (f∘f)(1) (f \circ f)(1) , which means f(f(1)) f(f(1)) .

STEP 2

1. Evaluate f(1) f(1) .
2. Substitute the result from Step 1 into f(x) f(x) to find f(f(1)) f(f(1)) .
3. Simplify the expression to find the final answer.

STEP 3

Evaluate f(1) f(1) by substituting x=1 x = 1 into the function:
f(1)=141+5 f(1) = \frac{14}{1+5}

STEP 4

Simplify the expression:
f(1)=146 f(1) = \frac{14}{6} f(1)=73 f(1) = \frac{7}{3}

STEP 5

Substitute f(1)=73 f(1) = \frac{7}{3} into f(x) f(x) to find f(f(1)) f(f(1)) :
f(73)=1473+5 f\left(\frac{7}{3}\right) = \frac{14}{\frac{7}{3} + 5}

STEP 6

Simplify the expression inside the denominator:
73+5=73+153=223 \frac{7}{3} + 5 = \frac{7}{3} + \frac{15}{3} = \frac{22}{3}

STEP 7

Substitute back into the function:
f(73)=14223 f\left(\frac{7}{3}\right) = \frac{14}{\frac{22}{3}}

STEP 8

Simplify the division by multiplying by the reciprocal:
f(73)=14×322 f\left(\frac{7}{3}\right) = 14 \times \frac{3}{22} f(73)=4222 f\left(\frac{7}{3}\right) = \frac{42}{22}

STEP 9

Simplify the fraction:
4222=2111 \frac{42}{22} = \frac{21}{11}
The value of (f∘f)(1) (f \circ f)(1) is:
2111 \boxed{\frac{21}{11}}

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