Question

NO LINKS!!
Please help me with #14.

Answer 1

a) Domain: (-∞, 10)

b) k⁻¹(8) = 6

c) CBD

d) Range: (-∞, 7)

e) k⁻¹(0) = 4

f) x = -5

Explanation:

Part a

The domain of the inverse of a function is the same as the range of the original function.

Therefore, the domain of the inverse function is:

• (-∞, 10)

Part b

The inverse of a function is its reflection in the line y = x.

Therefore, given that function k(6) = 8 then:

• k⁻¹(8) = 6

Part c

The inverse of a function is its reflection in the line y = x.

We cannot find k⁻¹(-9) since we have not been given the value of x when k(x) = -9.

Part d

The range of the inverse of a function is the same as the domain of the original function.

Therefore, the range of the inverse function is:

• (-∞, 7)

Part e

The inverse of a function is its reflection in the line y = x.

Therefore, given that function k(4) = 0 then:

• k⁻¹(0) = 4

Part f

The zero of the inverse function is the y-intercept of the original function. Therefore, given that k(0) = -5 then:

• k⁻¹(-5) = 0

Therefore, x = -5 is a zero of k⁻¹(x).