Question

Find the x- and y-intercepts of the function f(x)=log(2x+1)−1.

A) x-intercept: 0, y-intercept: -1
B) x-intercept: -1/2, y-intercept: -1
C) x-intercept: 1/2, y-intercept: -1
D) x-intercept: -1, y-intercept: 0

Answer 1

To find the x-intercept of f(x)=log(2x+1)−1, we solve for x when f(x)=0, but none of the options provided match the correct value x = 4.5. For the y-intercept, we set x to 0 and find f(0) = log(1) − 1, which is −1. Due to a likely typo in the options, we can confirm the y-intercept but not the x-intercept.

Step-by-step explanation:

To find the x-intercept of the function f(x)=log(2x+1)−1, we set f(x) to 0 and solve for x:

0 = log(2x+1) − 1

log(2x+1) = 1

2x + 1 = 101

2x = 9

x = 4.5

However, this solution does not match any of the options provided, suggesting that there may have been a typo or misunderstanding in the question or options.

To find the y-intercept, we set x to 0:

f(0) = log(2(0)+1) − 1

= log(1) − 1

= 0 − 1

= −1

Therefore, the y-intercept is −1, which matches some of the options provided. So, the correct y-intercept is −1, but we cannot confirm the x-intercept with the given options.