Math  /  Algebra

QuestionA particular function takes an input, squares it and then adds 1 to the new value to complete the output. What are possible inputs and outputs of this function? Select ALL that apply. input 3, output 8 input 4, output 17 input 8 , output 65 input 9 , output 80 input 12 , output 145 input 15 , output 225

Studdy Solution

STEP 1

1. The function takes an input x x , squares it, and then adds 1 to produce the output.
2. We need to verify which input-output pairs satisfy this function.

STEP 2

1. Define the function based on the problem statement.
2. Verify each input-output pair against the function.

STEP 3

Define the function f(x)=x2+1 f(x) = x^2 + 1 .

STEP 4

Verify the input-output pair: input 3, output 8.
Calculate f(3)=32+1=9+1=10 f(3) = 3^2 + 1 = 9 + 1 = 10 .
The output is 10, not 8. Therefore, this pair does not satisfy the function.

STEP 5

Verify the input-output pair: input 4, output 17.
Calculate f(4)=42+1=16+1=17 f(4) = 4^2 + 1 = 16 + 1 = 17 .
The output is 17, which matches. Therefore, this pair satisfies the function.

STEP 6

Verify the input-output pair: input 8, output 65.
Calculate f(8)=82+1=64+1=65 f(8) = 8^2 + 1 = 64 + 1 = 65 .
The output is 65, which matches. Therefore, this pair satisfies the function.

STEP 7

Verify the input-output pair: input 9, output 80.
Calculate f(9)=92+1=81+1=82 f(9) = 9^2 + 1 = 81 + 1 = 82 .
The output is 82, not 80. Therefore, this pair does not satisfy the function.

STEP 8

Verify the input-output pair: input 12, output 145.
Calculate f(12)=122+1=144+1=145 f(12) = 12^2 + 1 = 144 + 1 = 145 .
The output is 145, which matches. Therefore, this pair satisfies the function.

STEP 9

Verify the input-output pair: input 15, output 225.
Calculate f(15)=152+1=225+1=226 f(15) = 15^2 + 1 = 225 + 1 = 226 .
The output is 226, not 225. Therefore, this pair does not satisfy the function.
The input-output pairs that satisfy the function are:
- input 4, output 17 - input 8, output 65 - input 12, output 145

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