Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If f(1)=1 and f(n)=f(n-1)-1 then find the value of f(5). Answer:

If f(1)=1 f(1)=1 and f(n)=f(n−1)−1 f(n)=f(n-1)-1 then find the value of f(5) f(5) .\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Evaluate functionsright chevron icon

Full solution

Q. If f(1)=1 f(1)=1 and f(n)=f(n−1)−1 f(n)=f(n-1)-1 then find the value of f(5) f(5) .\newlineAnswer:
  1. Base Case Given: We are given that f(1)=1f(1) = 1. This is our base case.
  2. Recursive Formula: We are also given a recursive formula: f(n)=f(n−1)−1f(n) = f(n-1) - 1. This means that to find f(n)f(n), we subtract 11 from the value of ff at the previous integer, which is f(n−1)f(n-1).
  3. Finding f(5)f(5): To find f(5)f(5), we need to find the values of f(4)f(4), f(3)f(3), f(2)f(2), and we already know f(1)f(1).
  4. Calculating f(2)f(2): Using the recursive formula, f(2)=f(1)−1f(2) = f(1) - 1. Since f(1)=1f(1) = 1, we have f(2)=1−1=0f(2) = 1 - 1 = 0.
  5. Calculating f(3)f(3): Next, f(3)=f(2)−1f(3) = f(2) - 1. We found that f(2)=0f(2) = 0, so f(3)=0−1=−1f(3) = 0 - 1 = -1.
  6. Calculating f(4)f(4): Then, f(4)=f(3)−1f(4) = f(3) - 1. We found that f(3)=−1f(3) = -1, so f(4)=−1−1=−2f(4) = -1 - 1 = -2.
  7. Calculating f(5)f(5): Finally, f(5)=f(4)−1f(5) = f(4) - 1. We found that f(4)=−2f(4) = -2, so f(5)=−2−1=−3f(5) = -2 - 1 = -3.

More problems from Evaluate functions

Question
What is the domain of this function?\newline(9,–2)(6,–10)(–3,9)(5,2)(9,–2)(6,–10)(–3,9)(5,2)\newlineChoices:\newline(A){–3,5,6,9}(B){–10,–2,2,9}(C){2,5,6,9}(D){–6,–3,5,9}(A)\{–3,5,6,9\}\newline(B)\{–10,–2,2,9\}\newline(C)\{2,5,6,9\}\newline(D)\{–6,–3,5,9\}
Get tutor helpright-arrow

Posted 1 month ago

Question
Look at this set of ordered pairs:\newline(2,14)(2, 14)\newline(10,12)(10, 12)\newline(3,−19)(3, -19)\newlineIs this relation a function?\newlineChoices:\newline[[yes]\text{[[yes]}[no]]\text{[no]]}
Get tutor helpright-arrow

Posted 1 month ago

Question
Use the following function rule to find f(11) f(11) .\newlinef(x)=−10−7x f(x) = -10 - 7x \newlinef(11)= f(11) = _____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the slope of the line y=−3x−25 y = -3x - \frac{2}{5} .\newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 1 month ago

Question
A line has a slope of 33 and passes through the point (−2,−10)(-2,-10). Write its equation in slope-intercept form.\newlineWrite your answer using integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the range of this function?\newliney = |x|\newlineChoices:\newlineall real numbers\text{all real numbers}\newline{y∣y≥0}\{y \mid y \geq 0\}\newline{y∣y≤0}\{y \mid y \leq 0\}\newline{y∣y>0}\{y \mid y > 0\}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 1 1 unit down of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the domain of this function?\newline(8,–1)(7,–11)(–4,10)(4,3)(8,–1)(7,–11)(–4,10)(4,3)\newlineChoices: \newline(A){–4,4,7,8}(A)\{–4,4,7,8\}\newline(B){–11,–1,3,10}(B)\{–11,–1,3,10\}\newline(C){3,4,7,8}(C)\{3,4,7,8\}\newline(D){–7,–4,4,8}(D)\{–7,–4,4,8\}
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the domain of this function?\newline(10, –3)(2, –9)(–5, 8)(3, 1)(10,\,–3)(2,\,–9)(–5,\,8)(3,\,1)\newlineChoices:\newline[{–5,2,3,10}][{–9, –3,1,8}][{1,2,3,10}][{–10, –5,2,3}][\{–5,2,3,10\}][\{–9,\,–3,1,8\}][\{1,2,3,10\}][\{–10,\,–5,2,3\}]
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the domain of this function?\newline(1,–4)(9,–12)(–6,11)(7,5)(1,–4)(9,–12)(–6,11)(7,5)\newlineChoices:(A){–6,1,7,9}\newline\\(A)\{–6,1,7,9\}\newline(B){–12,–4,5,11}(B)\{–12,–4,5,11\}\newline(C{5,1,7,9}(C\{5,1,7,9\}\newline(D){–9,–6,1,7}(D)\{–9,–6,1,7\}
Get tutor helpright-arrow

Posted 1 month ago

View all (109)