How to find the (implicit) domain for the function f(x) = ln(16x + 14).
To find the implicit domain for the function f(x) = ln(16x + 14), we need to consider the restrictions on the input value, x, that will keep the function defined.
The function ln(16x + 14) is defined only for values of x that make the argument inside the natural logarithm positive. In other words, the expression 16x + 14 must be greater than zero.
To find the range of x that satisfies this condition, we can set up an inequality:
16x + 14 > 0
Now, let's solve this inequality to find the valid range for x:
First, subtract 14 from both sides of the inequality:
16x > -14
Next, divide both sides of the inequality by 16:
x > -14/16
Simplifying the expression, we have:
x > -7/8
So, the implicit domain for the function f(x) = ln(16x + 14) is x > -7/8. This means that any value of x greater than -7/8 will keep the function defined.