Final answer:
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.