Craig Lynch
01/05/2024 · Junior High School
Given the function \( f(x)=2 x-1 \), evaluate and simplify the following: \( f(x+h)= \) \( \frac{f(x+h)-f(x)}{h}=\square \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To evaluate \( f(x+h) \) for the function \( f(x) = 2x - 1 \), we substitute \( x+h \) into the function:
\[
f(x+h) = 2(x+h) - 1
\]
Now, simplify this expression:
\[
f(x+h) = 2x + 2h - 1
\]
Next, we need to evaluate \( \frac{f(x+h) - f(x)}{h} \). First, we calculate \( f(x) \):
\[
f(x) = 2x - 1
\]
Now, we can find \( f(x+h) - f(x) \):
\[
f(x+h) - f(x) = (2x + 2h - 1) - (2x - 1)
\]
Simplifying this gives:
\[
f(x+h) - f(x) = 2x + 2h - 1 - 2x + 1 = 2h
\]
Now, we can substitute this result into the expression \( \frac{f(x+h) - f(x)}{h} \):
\[
\frac{f(x+h) - f(x)}{h} = \frac{2h}{h}
\]
Assuming \( h \neq 0 \), we can simplify this to:
\[
\frac{f(x+h) - f(x)}{h} = 2
\]
Thus, the final results are:
\[
f(x+h) = 2x + 2h - 1
\]
\[
\frac{f(x+h) - f(x)}{h} = 2
\]
Quick Answer
\( f(x+h) = 2x + 2h - 1 \)
\( \frac{f(x+h) - f(x)}{h} = 2 \)
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit