Question

Create a formula for a function f(x) that has f(6) = 7. Do not give a simple constant function (like f(x) = 7) as your answer.

a. f(x)=2x−5

b. f(x)=x^2+1

c. f(x)=3⋅2^x−5

d. f(x)=x+1
​

Answer 1

Both options a, f(x)=2x-5, and d, f(x)=x+1, satisfy the condition that f(6) equals 7, therefore they are correct answers for creating a function f(x) with the desired property.

Step-by-step explanation:

To create a formula for a function f(x) that satisfies the condition f(6) = 7 without resorting to a simple constant function, we can evaluate the given options by substituting x with 6 and checking which one yields 7.

1. f(x)=2x−5: Substituting x with 6, we get f(6)=2(6)−5=12−5=7. This function meets the criteria and thus is a correct answer.
2. f(x)=x²+1: Trying to insert 6, we find that f(6)=6²+1=36+1=37, which does not meet the condition.
3. f(x)=3⋅2ˣ−5: Here, f(6)=3⋅2ˣ−5 does not equal 7, as the exponential term increases steeply.
4. f(x)=x+1: Substituting 6, we get f(6)=6+1=7, which also satisfies the required condition.

Therefore, both Option a, f(x)=2x−5, and Option d, f(x)=x+1, satisfy the condition that when x is 6, f(x) equals 7.