Determine the range of the inverse of f(x) = 2x + 1

The range is all real numbers for the inverse

Step-by-step explanation:

f(x) = 2x+1

The domain is all real numbers

The range is all real numbers

For the inverse, the domain becomes the range

The range becomes the domain

The domain is all real numbers

The range is all real numbers

Step-by-step explanation:

Given the function f(x) = 2x + 1

find : the range of the inverse of f(x) = 2x + 1

solutions:

f(x) = 2x + 1

y = 2x + 1

2x = y - 1

x = (y -1)/2

f~¹(x) = (x-1) /2

since the denominator is the constant number, so the range of function is all Real numbers

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°