If $f(x+1)=f(x)+1$ for all values of $x,$ and $f(7)=3,$ what is the value of $f(3)?$

VJesus12 wrote: ↑
Thu Oct 29, 2020 11:47 am
If $f(x+1)=f(x)+1$ for all values of $x,$ and $f(7)=3,$ what is the value of $f(3)?$

A. -1
B. 3
C. 7
D. 11
E. 13

Answer: A

Source: Veritas Prep

f(x+1) = f(x) + 1
f(7) = f (6+1) = f(6) + 1 = 3 ---> f(6) = 2
f(6) = f (5+1) = f(5) + 1 = 2 ---> f(5) = 1
f(5) = f (4+1) = f(4) + 1 = 2 ---> f(4) = 0
f(4) = f (3+1) = f(3) + 1 = 2 ---> f(3) = -1

Option A is the answer.

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Re: If $f(x+1)=f(x)+1$ for all values of $x,$ and $f(7)=3,$ what is the value of $f(3)?$

by Scott@TargetTestPrep » Thu Nov 12, 2020 7:37 am

VJesus12 wrote: ↑
Thu Oct 29, 2020 11:47 am
If $f(x+1)=f(x)+1$ for all values of $x,$ and $f(7)=3,$ what is the value of $f(3)?$

A. -1
B. 3
C. 7
D. 11
E. 13

Answer: A

Solution:

Letting x = 6, we have:

f(6 + 1) = f(6) + 1

f(7) = f(6) + 1

3 = f(6) + 1

2 = f(6)

Now letting x = 5, we have:

f(5 + 1) = f(5) + 1

f(6) = f(5) + 1

2 = f(5) + 1

1 = f(5)

Using the same argument, we see that f(4) = 0 and f(3) = -1.

Answer: A

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