Question

• The range of f is the domain of g and the domain of f is the range of g.
•

f(a) = b if and only if g(b) = a.

•

(a, b) is on the graph of f if and only if (b, a) is on the graph of g.

The function

f(x) = x³ + 7x + 5

is one-to-one. Since finding a formula for its inverse is beyond the scope of this textbook, use Properties of Inverse Functions Theorem to help you compute

f ⁻¹(5), f ⁻¹(13), and f ⁻¹(−3).

f −1(5)	=
f −1(13)	=
f −1(−3)	=

Answer 1

Given

To find , put and solve for x.

ie,

ie, or

For , which is impossible for real numbers. (Square of all real numbers will be positive)

Therefore

Similarly to find put

ie,

ie

or (This quadratic equation will have imaginary roots, so no need to consider this)

Therefore,

ie,

Now put

ie

or (This quadratic equation will have imaginary roots, so no need to consider this)

Therefore,

ie,