Question

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

The x-intercept of the function f(x) = log(2x + 1) − 1 is

. Its y-intercept is

.

Answer 1

The y-intercept is -1

The x-intercept is 4.5

Explanation:

We have the following equation:

f(x) = log(2x+1) - 1

The y intercept is the value of f(x) when x is equal to 0, so replacing x by 0 and solving for f(x), we get:

f(0) = log(2*0 + 1 ) -1

f(0) = log(1) - 1

f(0) = 0 - 1 = -1

Additionally, the x-intercept is the value of x when f(x) is equal to 0. So, replacing f(x) by 0 and solving for x, we get:

`0 = log(2x + 1) - 1\\1 = log(2x + 1)\\10^1=10^(log(2x + 1))\\10 = 2x + 1\\10 - 1 = 2x\\4.5 = x`